Log in

Relevant bibliographies by topics / Algebra / Journal articles

Journal articles on the topic 'Algebra'

To see the other types of publications on this topic, follow the link: Algebra.

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Algebra.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Radfar, A., and A. Rezaei. "Pseudo-BI-algebras‎: ‎Non-commutative generalization of BI-algebras." Journal of Algebraic Hyperstructures and Logical Algebras 4, no. 2 (2023): 167–87. http://dx.doi.org/10.61838/kman.jahla.4.2.11.

Full text

Abstract:

We ‎define and study the pseudo BI-algebras as a generalization of BI-algebras and implication algebras and investigate some properties‎. Also‎, ‎we define distributive pseudo BI-algebras and construct a BI-algebra related to these‎. ‎Further‎, ‎we prove ‎there is no proper pseudo BI-algebra of the order less than 4 and that every pseudo BI-algebra of order 4 is a poset‎, ‎and so is a pseudo BH-algebra‎. ‎‎Beside‎, ‎we introduce exchangeable pseudo BI-algebra and show that the class of them is a proper subclass of the class pseudo CI-algebras‎. ‎Finally‎, ‎we define the notions of (weak) commutative pseudo BI-algebras and prove ‎every weak commutative pseudo BI-algebra is a (dual) pseudo BH-algebra‎, ‎but the converse is not true‎, ‎and show that every exchangeable commutative pseudo BI-algebra is an implication algebra.

APA, Harvard, Vancouver, ISO, and other styles

2

Grigoryan, S. A., and T. V. Tonev. "Blaschke inductive limits of uniform algebras." International Journal of Mathematics and Mathematical Sciences 27, no. 10 (2001): 599–620. http://dx.doi.org/10.1155/s0161171201006792.

Full text

Abstract:

We consider and studyBlaschke inductive limit algebrasA(b), defined as inductive limits of disc algebrasA(D)linked by a sequenceb={Bk}k=1∞of finite Blaschke products. It is well known that bigG-disc algebrasAGover compact abelian groupsGwith ordered dualsΓ=Gˆ⊂ℚcan be expressed as Blaschke inductive limit algebras. Any Blaschke inductive limit algebraA(b)is a maximal and Dirichlet uniform algebra. Its Shilov boundary∂A(b)is a compact abelian group with dual group that is a subgroup ofℚ. It is shown that a bigG-disc algebraAGover a groupGwith ordered dualGˆ⊂ℝis a Blaschke inductive limit algebra if and only ifGˆ⊂ℚ. The local structure of the maximal ideal space and the set of one-point Gleason parts of a Blaschke inductive limit algebra differ drastically from the ones of a bigG-disc algebra. These differences are utilized to construct examples of Blaschke inductive limit algebras that are not bigG-disc algebras. A necessary and sufficient condition for a Blaschke inductive limit algebra to be isometrically isomorphic to a bigG-disc algebra is found. We consider also inductive limitsH∞(I)of algebrasH∞, linked by a sequenceI={Ik}k=1∞of inner functions, and prove a version of the corona theorem with estimates for it. The algebraH∞(I)generalizes the algebra of bounded hyper-analytic functions on an open bigG-disc, introduced previously by Tonev.

APA, Harvard, Vancouver, ISO, and other styles

3

Angeltveit, Vigleik. "Uniqueness of MoravaK-theory." Compositio Mathematica 147, no. 2 (September 27, 2010): 633–48. http://dx.doi.org/10.1112/s0010437x10005026.

Full text

Abstract:

AbstractWe show that there is an essentially uniqueS-algebra structure on the MoravaK-theory spectrumK(n), whileK(n) has uncountably manyMUor$\widehat {E(n)}$-algebra structures. Here$\widehat {E(n)}$is theK(n)-localized Johnson–Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space ofA∞structures on a spectrum, and use the theory ofS-algebrak-invariants for connectiveS-algebras found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol.6(2006), 1785–1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.

APA, Harvard, Vancouver, ISO, and other styles

4

Kassem, M. S., and K. Rowlands. "Double multipliers andA*-algebras of the first kind." Mathematical Proceedings of the Cambridge Philosophical Society 102, no. 3 (November 1987): 507–16. http://dx.doi.org/10.1017/s0305004100067554.

Full text

Abstract:

LetAbe anA*-algebra and letdenote its auxiliary norm closure. The multiplier algebras of dualA*-algebras of the first kind have been studed by Tomiuk [12], [13] and Wong[15]. In this paper we study the double multiplier algebra ofA*-algebras of the first kind. In particular, we prove that, ifAis anA*-algebra of the first kind, then the double multiplier algebraM(A) ofAis *-isomorphic and (auxiliary norm) isometric to a subalgebra ofM(), extending in the process some results established by Tomiuk[12]. We also consider the embedding of the double multiplier algebra ofAin**, when the latter is regarded as an algebra with the Arens product, and, in particular, we show that, for an annihilator A*-algebra,M(A) is *-isomorphic and (auxiliary norm) isometric to**.

APA, Harvard, Vancouver, ISO, and other styles

5

Caprau, Carmen. "Twin TQFTs and Frobenius Algebras." Journal of Mathematics 2013 (2013): 1–25. http://dx.doi.org/10.1155/2013/407068.

Full text

Abstract:

We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on atwin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra(C,W,z,z∗)consists of a commutative Frobenius algebraC, a symmetric Frobenius algebraW, and an algebra homomorphismz:C→Wwith dualz∗:W→C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category.

APA, Harvard, Vancouver, ISO, and other styles

6

Padhan, Rudra Narayan, and K. C. Pati. "Some studies on central derivation of nilpotent Lie superalgebra." Asian-European Journal of Mathematics 13, no. 04 (December 7, 2018): 2050068. http://dx.doi.org/10.1142/s1793557120500680.

Full text

Abstract:

Many theorems and formulas of Lie superalgebras run quite parallel to Lie algebras, sometimes giving interesting results. So it is quite natural to extend the new concepts of Lie algebra immediately to Lie superalgebra case as the later type of algebras have wide applications in physics and related theories. Using the concept of isoclinism, Saeedi and Sheikh-Mohseni [A characterization of stem algebras in terms of central derivations, Algebr. Represent. Theory 20 (2017) 1143–1150; On [Formula: see text]-derivations of Filippov algebra, to appear in Asian-Eur. J. Math.; S. Sheikh-Mohseni, F. Saeedi and M. Badrkhani Asl, On special subalgebras of derivations of Lie algebras, Asian-Eur. J. Math. 8(2) (2015) 1550032] recently studied the central derivation of nilpotent Lie algebra with nilindex 2. The purpose of the present paper is to continue and extend the investigation to obtain some similar results for Lie superalgebras, as isoclinism in Lie superalgebra is being recently introduced.

APA, Harvard, Vancouver, ISO, and other styles

7

Feeman, Timothy G. "The Bourgain algebra of a nest algebra." Proceedings of the Edinburgh Mathematical Society 40, no. 1 (February 1997): 151–66. http://dx.doi.org/10.1017/s0013091500023518.

Full text

Abstract:

In analogy with a construction from function theory, we herein define right, left, and two-sided Bourgain algebras associated with an operator algebra A. These algebras are defined initially in Banach space terms, using the weak-* topology on A, and our main result is to give a completely algebraic characterization of them in the case where A is a nest algebra. Specifically, if A = alg N is a nest algebra, we show that each of the Bourgain algebras defined has the form A + K ∩ B, where B is the nest algebra corresponding to a certain subnest of N. We also characterize algebraically the second-order (and higher) Bourgain algebras of a nest algebra, showing for instance that the second-order two-sided Bourgain algebra coincides with the two-sided Bourgain algebra itself in this case.

APA, Harvard, Vancouver, ISO, and other styles

8

BOKUT, L. A., YUQUN CHEN, and QIUHUI MO. "GRÖBNER–SHIRSHOV BASES AND EMBEDDINGS OF ALGEBRAS." International Journal of Algebra and Computation 20, no. 07 (November 2010): 875–900. http://dx.doi.org/10.1142/s0218196710005923.

Full text

Abstract:

In this paper, by using Gröbner–Shirshov bases, we show that in the following classes, each (respectively, countably generated) algebra can be embedded into a simple (respectively, two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded into a simple two-generated algebra: associative algebras, semigroups, Lie algebras, associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We give another proofs of the well known theorems: each countably generated group (respectively, associative algebra, semigroup, Lie algebra) can be embedded into a two-generated group (respectively, associative algebra, semigroup, Lie algebra).

APA, Harvard, Vancouver, ISO, and other styles

9

Xin, Xiao-Long, and Pu Wang. "States and Measures on Hyper BCK-Algebras." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/397265.

Full text

Abstract:

We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra(H,∘,0,e)and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a∘-compatibledregular congruence relationθand aθ-compatibledinf-Bosbach stateson(H,∘,0,e). By inducing an inf-Bosbach states^on the quotient structureH/[0]θ, we show thatH/[0]θis a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebraH/Ker(m)by a reflexive hyper BCK-idealKer(m). Further, we prove thatH/Ker(m)is a bounded commutative BCK-algebra.

APA, Harvard, Vancouver, ISO, and other styles

10

Patlertsin, Sutida, Suchada Pongprasert, and Thitarie Rungratgasame. "On Inner Derivations of Leibniz Algebras." Mathematics 12, no. 8 (April 11, 2024): 1152. http://dx.doi.org/10.3390/math12081152.

Full text

Abstract:

Leibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras. In this work, we demonstrate that the algebra of inner derivations of a Leibniz algebra can be decomposed into the sum of the algebra of left multiplications and a certain ideal. Furthermore, we show that the quotient of the algebra of derivations of the Leibniz algebra by this ideal yields a complete Lie algebra. Our results independently establish that any derivation of a semisimple Leibniz algebra can be expressed as a combination of three derivations. Additionally, we compare the properties of the algebra of inner derivations of Leibniz algebras with the algebra of central derivations.

APA, Harvard, Vancouver, ISO, and other styles

11

Nahlus, Nazih. "Lie Algebras of Pro-Affine Algebraic Groups." Canadian Journal of Mathematics 54, no. 3 (June 1, 2002): 595–607. http://dx.doi.org/10.4153/cjm-2002-021-9.

Full text

Abstract:

AbstractWe extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed fieldKof characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra ℒ(G) of the pro-affine algebraic groupGoverK, which is discrete in the finite-dimensional case and linearly compact in general. As an example, ifLis any sub Lie algebra of ℒ(G), we show that the closure of [L,L] in ℒ(G) is algebraic in ℒ(G).We also discuss the Hopf algebra of representative functions H(L) of a residually finite dimensional Lie algebraL. As an example, we show that ifLis a sub Lie algebra of ℒ(G) andGis connected, then the canonical Hopf algebra morphism fromK[G] intoH(L) is injective if and only ifLis algebraically dense in ℒ(G).

APA, Harvard, Vancouver, ISO, and other styles

12

Choi, Seul Hee, Jongwoo Lee, and Ki-Bong Nam. "Algebra Versus Its Anti-symmetric Algebra." Algebra Colloquium 16, no. 04 (December 2009): 661–68. http://dx.doi.org/10.1142/s1005386709000625.

Full text

Abstract:

For a given algebra A= 〈A,+,·〉, we can define its anti-symmetric algebra A-= 〈A-,+,[ , ]〉 using the commutator [ , ] of A, where the sets A and A- are the same. We show that there are isomorphic algebras A1 and A2 such that their anti-symmetric algebras are not isomorphic. We define a special type Lie algebra and show that it is simple.

APA, Harvard, Vancouver, ISO, and other styles

13

Bustamante, Miguel D., Pauline Mellon, and M. Victoria Velasco. "Determining When an Algebra Is an Evolution Algebra." Mathematics 8, no. 8 (August 12, 2020): 1349. http://dx.doi.org/10.3390/math8081349.

Full text

Abstract:

Evolution algebras are non-associative algebras that describe non-Mendelian hereditary processes and have connections with many other areas. In this paper, we obtain necessary and sufficient conditions for a given algebra A to be an evolution algebra. We prove that the problem is equivalent to the so-called SDC problem, that is, the simultaneous diagonalisation via congruence of a given set of matrices. More precisely we show that an n-dimensional algebra A is an evolution algebra if and only if a certain set of n symmetric n×n matrices {M1,…,Mn} describing the product of A are SDC. We apply this characterisation to show that while certain classical genetic algebras (representing Mendelian and auto-tetraploid inheritance) are not themselves evolution algebras, arbitrarily small perturbations of these are evolution algebras. This is intringuing, as evolution algebras model asexual reproduction, unlike the classical ones.

APA, Harvard, Vancouver, ISO, and other styles

14

Hwang, In Ho, Yong Lin Liu, and Hee Sik Kim. "On BV-Algebras." Mathematics 8, no. 10 (October 14, 2020): 1779. http://dx.doi.org/10.3390/math8101779.

Full text

Abstract:

In this paper, we introduce the notion of a BV-algebra, and we show that a BV-algebra is logically equivalent to several algebras, i.e., BM-algebras, BT-algebras, BO-algebras and 0-commutative B-algebras. Moreover, we show that a BV-algebra with (F) is logically equivalent to several algebras, and we show some relationships between a BV-algebra with (F) and several related algebras.

APA, Harvard, Vancouver, ISO, and other styles

15

Chen, Quanguo, and Yong Deng. "Hopf algebra structures on generalized quaternion algebras." Electronic Research Archive 32, no. 5 (2024): 3334–62. http://dx.doi.org/10.3934/era.2024154.

Full text

Abstract:

<abstract><p>In this paper, we use elementary linear algebra methods to explore possible Hopf algebra structures within the generalized quaternion algebra. The sufficient and necessary conditions that make the generalized quaternion algebra a Hopf algebra are given. It is proven that not all of the generalized quaternion algebras have Hopf algebraic structures. When the generalized quaternion algebras have Hopf algebraic structures, we describe all the Hopf algebra structures. Finally, we shall prove that all the Hopf algebra structures on the generalized quaternion algebras are isomorphic to Sweedler Hopf algebra, which is consistent with the classification of 4-dimensional Hopf algebras.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

16

Chtioui, T., S. Mabrouk, and A. Makhlouf. "Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras." Extracta Mathematicae 38, no. 1 (June 1, 2023): 27–50. http://dx.doi.org/10.17398/2605-5686.38.1.27.

Full text

Abstract:

The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra.

APA, Harvard, Vancouver, ISO, and other styles

17

LI, HAISHENG. "VERTEX ALGEBRAS AND VERTEX POISSON ALGEBRAS." Communications in Contemporary Mathematics 06, no. 01 (February 2004): 61–110. http://dx.doi.org/10.1142/s0219199704001264.

Full text

Abstract:

This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general construction theorems of vertex Poisson algebras are given. A notion of filtered vertex algebra is formulated in terms of a notion of good filtration and it is proved that the associated graded vector space of a filtered vertex algebra is naturally a vertex Poisson algebra. For any vertex algebra V, a general construction and a classification of good filtrations are given. To each ℕ-graded vertex algebra V=∐n∈ℕV(n) with [Formula: see text], a canonical (good) filtration is associated and certain results about generating subspaces of certain types of V are also obtained. Furthermore, a notion of formal deformation of a vertex (Poisson) algebra is formulated and a formal deformation of vertex Poisson algebras associated with vertex Lie algebras is constructed.

APA, Harvard, Vancouver, ISO, and other styles

18

Shwan Adnan Bajalan, Rasti Raheem Mohammed Amin, and Aram K. Bajalan. "Structures of Pseudo - BG Algebra and Sime pseudo – BG - Algebra." Tikrit Journal of Pure Science 27, no. 3 (November 29, 2022): 73–77. http://dx.doi.org/10.25130/tjps.v27i3.48.

Full text

Abstract:

In this paper, we introduced the notion new types of algebras pseudo BG- algebra, pseudo sub BG –algebra, Pseudo Ideal and pseudo strong Ideal of Pseudo-BG-Algebras. We state some Proposition and examples which determine the relationships between these notions and some types of ideal and we introduced the notion semi pseudo BG- algebra, pseudo sub BG –algebra, Pseudo Ideal and pseudo strong Ideal of semi pseudo-BG-Algebras. We investigated a new notion, of algebra called semi pseudo BG- algebra. We state some Proposition and examples which determine the relationships between these notions and some types of ideals defined minimal and homomorphism and kernel.

APA, Harvard, Vancouver, ISO, and other styles

19

BOKUT, L. A., YUQUN CHEN, and JIAPENG HUANG. "GRÖBNER–SHIRSHOV BASES FOR L-ALGEBRAS." International Journal of Algebra and Computation 23, no. 03 (April 16, 2013): 547–71. http://dx.doi.org/10.1142/s0218196713500094.

Full text

Abstract:

In this paper, we first establish Composition-Diamond lemma for Ω-algebras. We give a Gröbner–Shirshov basis of the free L-algebra as a quotient algebra of a free Ω-algebra, and then the normal form of the free L-algebra is obtained. Second we establish Composition-Diamond lemma for L-algebras. As applications, we give Gröbner–Shirshov bases of the free dialgebra and the free product of two L-algebras, and then we show four embedding theorems of L-algebras: (1) Every countably generated L-algebra can be embedded into a two-generated L-algebra. (2) Every L-algebra can be embedded into a simple L-algebra. (3) Every countably generated L-algebra over a countable field can be embedded into a simple two-generated L-algebra. (4) Three arbitrary L-algebras A, B, C over a field k can be embedded into a simple L-algebra generated by B and C if |k| ≤ dim (B * C) and |A| ≤ |B * C|, where B * C is the free product of B and C.

APA, Harvard, Vancouver, ISO, and other styles

20

Matsumoto, Kengo. "C*-algebras associated with presentations of subshifts ii. ideal structure and lambda-graph subsystems." Journal of the Australian Mathematical Society 81, no. 3 (December 2006): 369–85. http://dx.doi.org/10.1017/s1446788700014373.

Full text

Abstract:

AbstractA λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. InDoc. Math.7 (2002) 1–30, the author constructed aC*-algebraO£associated with a λ-graph system £ from a graph theoretic view-point. If a λ-graph system comes from a finite labeled graph, the algebra becomes a Cuntz-Krieger algebra. In this paper, we prove that there is a bijective correspondence between the lattice of all saturated hereditary subsets of £ and the lattice of all ideals of the algebraO£, under a certain condition on £ called (II). As a result, the class of theC*-algebras associated with λ-graph systems under condition (II) is closed under quotients by its ideals.

APA, Harvard, Vancouver, ISO, and other styles

21

Chaudhry, Muhammad Anwar, Asfand Fahad, Muhammad Imran Qureshi, and Urwa Riasat. "Some Results about Weak UP-algebras." Journal of Mathematics 2022 (September 16, 2022): 1–6. http://dx.doi.org/10.1155/2022/1206804.

Full text

Abstract:

We introduce a new class of algebras, weak UP-algebras, briefly written as WUP-algebras, as a wider class than the classes of UP-algebras and KU-algebras. We investigate fundamental aspects including maximal elements, branches and the subalgebra consisting of maximal elements of a WUP-algebra. We also study regular congruences on a WUP-algebra as well as the corresponding quotient WUP-algebras. We prove that the congruence generated from the branches of a WUP-algebra is regular and the corresponding quotient algebra χ / q is isomorphic to the WUP-algebra Max χ , the subalgebra of χ consisting of its maximal elements.

APA, Harvard, Vancouver, ISO, and other styles

22

Green, Edward L., and Sibylle Schroll. "Almost Gentle Algebras and their Trivial Extensions." Proceedings of the Edinburgh Mathematical Society 62, no. 2 (November 29, 2018): 489–504. http://dx.doi.org/10.1017/s001309151800055x.

Full text

Abstract:

AbstractIn this paper we define almost gentle algebras, which are monomial special multiserial algebras generalizing gentle algebras. We show that the trivial extension of an almost gentle algebra by its minimal injective co-generator is a symmetric special multiserial algebra and hence a Brauer configuration algebra. Conversely, we show that any almost gentle algebra is an admissible cut of a unique Brauer configuration algebra and, as a consequence, we obtain that every Brauer configuration algebra with multiplicity function identically one is the trivial extension of an almost gentle algebra. We show that a hypergraph is associated with every almost gentle algebra A, and that this hypergraph induces the Brauer configuration of the trivial extension of A. Among other things, this gives a combinatorial criterion to decide when two almost gentle algebras have isomorphic trivial extensions.

APA, Harvard, Vancouver, ISO, and other styles

23

Oudom, J. M., and D. Guin. "On the Lie enveloping algebra of a pre-Lie algebra." Journal of K-Theory 2, no. 1 (May 28, 2008): 147–67. http://dx.doi.org/10.1017/is008001011jkt037.

Full text

Abstract:

AbstractWe construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. It turns S(L) into a Hopf algebra which is isomorphic to the enveloping algebra of LLie. Then we prove that in the case of rooted trees our construction gives the Grossman-Larson Hopf algebra, which is known to be the dual of the Connes-Kreimer Hopf algebra. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees.

APA, Harvard, Vancouver, ISO, and other styles

24

Meng, Biao Long, and Xiao Long Xin. "A Note of Filters in Effect Algebras." Chinese Journal of Mathematics 2013 (November 10, 2013): 1–4. http://dx.doi.org/10.1155/2013/570496.

Full text

Abstract:

We investigate relations of the two classes of filters in effect algebras (resp., MV-algebras). We prove that a lattice filter in a lattice ordered effect algebra (resp., MV-algebra) does not need to be an effect algebra filter (resp., MV-filter). In general, in MV-algebras, every MV-filter is also a lattice filter. Every lattice filter in a lattice ordered effect algebra is an effect algebra filter if and only if is an orthomodular lattice. Every lattice filter in an MV-algebra is an MV-filter if and only if is a Boolean algebra.

APA, Harvard, Vancouver, ISO, and other styles

25

Wu, Xiaoying, and Xiaohong Zhang. "The Structure Theorems of Pseudo-BCI Algebras in Which Every Element is Quasi-Maximal." Symmetry 10, no. 10 (October 8, 2018): 465. http://dx.doi.org/10.3390/sym10100465.

Full text

Abstract:

For mathematical fuzzy logic systems, the study of corresponding algebraic structures plays an important role. Pseudo-BCI algebra is a class of non-classical logic algebras, which is closely related to various non-commutative fuzzy logic systems. The aim of this paper is focus on the structure of a special class of pseudo-BCI algebras in which every element is quasi-maximal (call it QM-pseudo-BCI algebras in this paper). First, the new notions of quasi-maximal element and quasi-left unit element in pseudo-BCK algebras and pseudo-BCI algebras are proposed and some properties are discussed. Second, the following structure theorem of QM-pseudo-BCI algebra is proved: every QM-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an anti-group pseudo-BCI algebra. Third, the new notion of weak associative pseudo-BCI algebra (WA-pseudo-BCI algebra) is introduced and the following result is proved: every WA-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an Abel group.

APA, Harvard, Vancouver, ISO, and other styles

26

Rump, Wolfgang. "Non-commutative effect algebras, L-algebras, and local duality." Mathematica Slovaca 74, no. 2 (April 1, 2024): 451–68. http://dx.doi.org/10.1515/ms-2024-0034.

Full text

Abstract:

Abstract GPE-algebras were introduced by Dvurečenskij and Vetterlein as unbounded pseudo-effect algebras. Recently, they have been characterized as partial L-algebras with local duality. In the present paper, GPE-algebras with an everywhere defined L-algebra operation are investigated. For example, linearly ordered GPE-algebra are of that type. They are characterized by their self-similar closures which are represented as negative cones of totally ordered groups. More generally, GPE-algebras with an everywhere defined multiplication are identified as negative cones of directed groups. If their partial L-algebra structure is globally defined, the enveloping group is lattice-ordered. For any self-similar L-algebra A, exponent maps are introduced, generalizing conjugation in the structure group. It is proved that the exponent maps are L-algebra automorphisms of A if and only if A is a GPE-algebra. As an application, a new characterization of cone algebras is obtained. Lattice GPE-algebras are shown to be equivalent to ∧-closed L-algebras with local duality.

APA, Harvard, Vancouver, ISO, and other styles

27

Hou, Dongping, Xiang Ni, and Chengming Bai. "Pre-jordan Algebras." MATHEMATICA SCANDINAVICA 112, no. 1 (March 1, 2013): 19. http://dx.doi.org/10.7146/math.scand.a-15231.

Full text

Abstract:

The purpose of this paper is to introduce and study a notion of pre-Jordan algebra. Pre-Jordan algebras are regarded as the underlying algebraic structures of the Jordan algebras with a nondegenerate symplectic form. They are the algebraic structures behind the Jordan Yang-Baxter equation and Rota-Baxter operators in terms of $\mathcal{O}$-operators of Jordan algebras introduced in this paper. Pre-Jordan algebras are analogues for Jordan algebras of pre-Lie algebras and fit into a bigger framework with a close relationship with dendriform algebras. The anticommutator of a pre-Jordan algebra is a Jordan algebra and the left multiplication operators give a representation of the Jordan algebra, which is the beauty of such a structure. Furthermore, we introduce a notion of $\mathcal{O}$-operator of a pre-Jordan algebra which gives an analogue of the classical Yang-Baxter equation in a pre-Jordan algebra.

APA, Harvard, Vancouver, ISO, and other styles

28

Oziewicz, Zbigniew, and William Stewart Page. "Frobenius algebra with relaxed associativity constraint." Journal of Knot Theory and Its Ramifications 27, no. 07 (June 2018): 1841008. http://dx.doi.org/10.1142/s0218216518410080.

Full text

Abstract:

Frobenius algebra is formulated within the Abelian monoidal category of operad of graphs. A not necessarily associative algebra [Formula: see text] is said to be a Frobenius algebra if there exists a [Formula: see text]-module isomorphism. A new concept of a solvable Frobenius algebra is introduced: an algebra [Formula: see text] is said to be a solvable Frobenius algebra if it possesses a nonzero one-sided [Formula: see text]-module morphism with nontrivial radical. In the category of operad of graphs, we can express the necessary and sufficient conditions for an algebra to be a solvable Frobenius algebra. The notion of a solvable Frobenius algebra makes it possible to find all commutative nonassociative Frobenius algebras (Conjecture 10.1), and to find all Frobenius structures for commutative associative Frobenius algebras. Frobenius algebra allows [Formula: see text]-permuted opposite algebra to be extended to [Formula: see text]-permuted algebras.

APA, Harvard, Vancouver, ISO, and other styles

29

AQUINO, R. M., E. N. MARCOS, and S. TREPODE. "ON THE EXISTENCE OF A DERIVED EQUIVALENCE BETWEEN A KOSZUL ALGEBRA AND ITS YONEDA ALGEBRA." Journal of Algebra and Its Applications 13, no. 04 (January 9, 2014): 1350136. http://dx.doi.org/10.1142/s0219498813501363.

Full text

Abstract:

In this paper, we study the derived categories of a Koszul algebra and its Yoneda algebra to determine when those categories are triangularly equivalent. We prove that the simply connected Koszul algebras are derived equivalent to their Yoneda algebras. We have considered discrete Koszul algebras and we gave necessary and sufficient conditions for those Koszul algebras to be derived equivalent to their Yoneda algebras. We also study the class of Koszul algebras which are derived equivalent to hereditary algebras. For the case where the hereditary algebra is tame, we characterized the derived equivalence between those Koszul algebras and their Yoneda algebras.

APA, Harvard, Vancouver, ISO, and other styles

30

Ouedraogo, Sidmanagde Emile, Souleymane Savadogo, and André Conseibo. "Evolution algebras that are almost Jordan." Gulf Journal of Mathematics 16, no. 2 (April 12, 2024): 100–110. http://dx.doi.org/10.56947/gjom.v16i2.1872.

Full text

Abstract:

In this paper, we give a necessary and sufficient condition for an almost Jordan algebra, which is also called Lie triple algebra to be an evolution algebra. We study the nilpotency, power associativity of such algebras. We specify the necessary and sufficient conditions for such an algebra to be baric. Along the way we show that train evolution algebras which are almost Jordan algebras are of rank at most 5. We prove that any finite-dimensional non-nil-evolution algebra verifying the identity of almost Jordan algebras has at least one non-zero idempotent. Finally, we study the derivations of this class of algebras.

APA, Harvard, Vancouver, ISO, and other styles

31

Grant, Joseph, and Osamu Iyama. "Higher preprojective algebras, Koszul algebras, and superpotentials." Compositio Mathematica 156, no. 12 (December 2020): 2588–627. http://dx.doi.org/10.1112/s0010437x20007538.

Full text

Abstract:

In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that the quiver of the higher preprojective algebra is obtained by adding arrows to the quiver of the original algebra, and these arrows can be read off from the last term of the bimodule resolution of the original algebra. In the Koszul case, we are able to obtain the new relations of the higher preprojective algebra by differentiating a superpotential and we show that when our original algebra is $d$-hereditary, all the relations come from the superpotential. We then construct projective resolutions of all simple modules for the higher preprojective algebra of a $d$-hereditary algebra. This allows us to recover various known homological properties of the higher preprojective algebras and to obtain a large class of almost Koszul dual pairs of algebras. We also show that when our original algebra is Koszul there is a natural map from the quadratic dual of the higher preprojective algebra to a graded trivial extension algebra.

APA, Harvard, Vancouver, ISO, and other styles

32

Brown, Lawrence G., James A. Mingo, and Nien-Tsu Shen. "Quasi-Multipliers and Embeddings of Hilbert C*-Bimodules." Canadian Journal of Mathematics 46, no. 06 (December 1994): 1150–74. http://dx.doi.org/10.4153/cjm-1994-065-5.

Full text

Abstract:

Abstract This paper considers Hilbert C*-bimodules, a slight generalization of imprimitivity bimodules which were introduced by Rieffel [20]. Brown, Green, and Rieffel [7] showed that every imprimitivity bimodule X can be embedded into a certain C*-algebra L, called the linking algebra of X. We consider arbitrary embeddings of Hilbert C*-bimodules into C*-algebras; i.e. we describe the relative position of two arbitrary hereditary C*-algebras of a C*-algebra, in an analogy with Dixmier's description [10] of the relative position of two subspaces of a Hilbert space. The main result of this paper (Theorem 4.3) is taken from the doctoral dissertation of the third author [22], although the proof here follows a different approach. In Section 1 we set out the definitions and basic properties (mostly folklore) of Hilbert C*-bimodules. In Section 2 we show how every quasi-multiplier gives rise to an embedding of a bimodule. In Section 3 we show that , the enveloping C*-algebra of the C*-algebraA with its product perturbed by a positive quasi-multiplier , is isomorphic to the closure (Proposition 3.1). Section 4 contains the main theorem (4.3), and in Section 5 we explain the analogy with the relative position of two subspaces of a Hilbert spaces and present some complements.

APA, Harvard, Vancouver, ISO, and other styles

33

Kirchberg, Eberhard, and Mikael Rørdam. "When central sequence C*-algebras have characters." International Journal of Mathematics 26, no. 07 (June 2015): 1550049. http://dx.doi.org/10.1142/s0129167x15500494.

Full text

Abstract:

We investigate C*-algebras whose central sequence algebra has no characters, and we raise the question if such C*-algebras necessarily must absorb the Jiang–Su algebra (provided that they also are separable). We relate this question to a question of Dadarlat and Toms if the Jiang–Su algebra always embeds into the infinite tensor power of any unital C*-algebra without characters. We show that absence of characters of the central sequence algebra implies that the C*-algebra has the so-called strong Corona Factorization Property, and we use this result to exhibit simple nuclear separable unital C*-algebras whose central sequence algebra does admit a character. We show how stronger divisibility properties on the central sequence algebra imply stronger regularity properties of the underlying C*-algebra.

APA, Harvard, Vancouver, ISO, and other styles

34

LIU, CHENG–KAI. "The structure of triple homomorphisms onto prime algebras." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 2 (October 23, 2018): 345–60. http://dx.doi.org/10.1017/s0305004118000737.

Full text

Abstract:

AbstractTriple homomorphisms on C*-algebras and JB*-triples have been studied in the literature. From the viewpoint of associative algebras, we characterise the structure of triple homomorphisms from an arbitrary ⋆-algebra onto a prime *-algebra. As an application, we prove that every triple homomorphism from a Banach ⋆-algebra onto a prime semisimple idempotent Banach *-algebra is continuous. The analogous results for prime C*-algebras and standard operator *-algebras on Hilbert spaces are also described.

APA, Harvard, Vancouver, ISO, and other styles

35

Poon, Yiu-Tung, and Zhong-Jin Ruan. "Operator Algebras with Contractive Approximate Identities." Canadian Journal of Mathematics 46, no. 2 (April 1, 1994): 397–414. http://dx.doi.org/10.4153/cjm-1994-021-0.

Full text

Abstract:

AbstractWe study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.

APA, Harvard, Vancouver, ISO, and other styles

36

Guo, Xiangqian, and Genqiang Liu. "Jet modules for the centerless Virasoro-like algebra." Journal of Algebra and Its Applications 18, no. 01 (January 2019): 1950002. http://dx.doi.org/10.1142/s0219498819500026.

Full text

Abstract:

In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a [Formula: see text]-torus. The jet modules are certain natural modules over the Lie algebra of semi-direct product of the centerless Virasoro-like algebra and the Laurent polynomial algebra in two variables. We reduce the irreducible jet modules to the finite-dimensional irreducible modules over some infinite-dimensional Lie algebra and then characterize the irreducible jet modules with irreducible finite dimensional modules over [Formula: see text]. To determine the indecomposable jet modules, we use the technique of polynomial modules in the sense of [Irreducible representations for toroidal Lie algebras, J. Algebras 221 (1999) 188–231; Weight modules over exp-polynomial Lie algebras, J. Pure Appl. Algebra 191 (2004) 23–42]. Consequently, indecomposable jet modules are described using modules over the algebra [Formula: see text], which is the “positive part” of a Block type algebra studied first by [Some infinite-dimensional simple Lie algebras in characteristic [Formula: see text] related to those of Block, J. Pure Appl. Algebra 127(2) (1998) 153–165] and recently by [A [Formula: see text]-graded generalization of the Witt-algebra, preprint; Classification of simple Lie algebras on a lattice, Proc. London Math. Soc. 106(3) (2013) 508–564]).

APA, Harvard, Vancouver, ISO, and other styles

37

Ait Ben Haddou, Malika, Saïd Benayadi, and Said Boulmane. "Malcev–Poisson–Jordan algebras." Journal of Algebra and Its Applications 15, no. 09 (August 22, 2016): 1650159. http://dx.doi.org/10.1142/s0219498816501590.

Full text

Abstract:

Malcev–Poisson–Jordan algebra (MPJ-algebra) is defined to be a vector space endowed with a Malcev bracket and a Jordan structure which are satisfying the Leibniz rule. We describe such algebras in terms of a single bilinear operation, this class strictly contains alternative algebras. For a given Malcev algebra [Formula: see text], it is interesting to classify the Jordan structure ∘ on the underlying vector space of [Formula: see text] such that [Formula: see text] is an MPJ-algebra (∘ is called an MPJ-structure on Malcev algebra [Formula: see text]. In this paper we explicitly give all MPJ-structures on some interesting classes of Malcev algebras. Further, we introduce the concept of pseudo-Euclidean MPJ-algebras (PEMPJ-algebras) and we show how one can construct new interesting quadratic Lie algebras and pseudo-Euclidean Malcev (non-Lie) algebras from PEMPJ-algebras. Finally, we give inductive descriptions of nilpotent PEMPJ-algebras.

APA, Harvard, Vancouver, ISO, and other styles

38

Phuapong, Sarawut, and Sorasak Leeratanavalee. "GENERALIZED DERIVED ALGEBRAS AND GENERALIZED INDUCED ALGEBRAS." Asian-European Journal of Mathematics 03, no. 03 (September 2010): 485–94. http://dx.doi.org/10.1142/s1793557110000295.

Full text

Abstract:

Substituting for the fundamental operations of an algebra term operations we get a new algebra of the same type, called a generalized derived algebra. Such substitutions are called generalized hypersubstitutions. Generalized hypersubstitutions can also be applied to every equation of a fully invariant equational theory. The equational theory generated by the resulting set of the equations induces on every algebra of the type under consideration a fully invariant congruence relation. If we factorize the generalized derived algebra by this fully invariant congruence relation we will obtain an algebra which we call generalized induced algebra. In this paper, we prove some properties which transfer the starting algebras to generalized derived algebras and to generalized induced algebras.

APA, Harvard, Vancouver, ISO, and other styles

39

BATES, TERESA, TOKE MEIER CARLSEN, and DAVID PASK. "-algebras of labelled graphs III—-theory computations." Ergodic Theory and Dynamical Systems 37, no. 2 (October 6, 2015): 337–68. http://dx.doi.org/10.1017/etds.2015.62.

Full text

Abstract:

In this paper we give a formula for the$K$-theory of the$C^{\ast }$-algebra of a weakly left-resolving labelled space. This is done by realizing the$C^{\ast }$-algebra of a weakly left-resolving labelled space as the Cuntz–Pimsner algebra of a$C^{\ast }$-correspondence. As a corollary, we obtain a gauge-invariant uniqueness theorem for the$C^{\ast }$-algebra of any weakly left-resolving labelled space. In order to achieve this, we must modify the definition of the$C^{\ast }$-algebra of a weakly left-resolving labelled space. We also establish strong connections between the various classes of$C^{\ast }$-algebras that are associated with shift spaces and labelled graph algebras. Hence, by computing the$K$-theory of a labelled graph algebra, we are providing a common framework for computing the$K$-theory of graph algebras, ultragraph algebras, Exel–Laca algebras, Matsumoto algebras and the$C^{\ast }$-algebras of Carlsen. We provide an inductive limit approach for computing the$K$-groups of an important class of labelled graph algebras, and give examples.

APA, Harvard, Vancouver, ISO, and other styles

40

Rezaei, Akbar, Arsham Borumand Saeid, and Andrzej Walendziak. "Some results on pseudo-Q algebras." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16, no. 1 (December 1, 2017): 61–72. http://dx.doi.org/10.1515/aupcsm-2017-0005.

Full text

Abstract:

AbstractThe notions of a dual pseudo-Q algebra and a dual pseudo-QC algebra are introduced. The properties and characterizations of them are investigated. Conditions for a dual pseudo-Q algebra to be a dual pseudo-QC algebra are given. Commutative dual pseudo-QC algebras are considered. The interrelationships between dual pseudo-Q/QC algebras and other pseudo algebras are visualized in a diagram.

APA, Harvard, Vancouver, ISO, and other styles

41

WANG, D. G., J. J. ZHANG, and G. ZHUANG. "COASSOCIATIVE LIE ALGEBRAS." Glasgow Mathematical Journal 55, A (October 2013): 195–215. http://dx.doi.org/10.1017/s001708951300058x.

Full text

Abstract:

AbstractA coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the usual universal enveloping algebra of a Lie algebra. This new enveloping algebra provides interesting examples of non-commutative and non-cocommutative Hopf algebras and leads to the classification of connected Hopf algebras of Gelfand–Kirillov dimension four in Wang et al. (Trans. Amer. Math. Soc., to appear).

APA, Harvard, Vancouver, ISO, and other styles

42

Bezhanishvili, Guram, and Patrick J. Morandi. "Profinite Heyting Algebras and Profinite Completions of Heyting Algebras." gmj 16, no. 1 (March 2009): 29–47. http://dx.doi.org/10.1515/gmj.2009.29.

Full text

Abstract:

Abstract This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to the profinite completion of a Heyting algebra (resp. bounded distributive lattice). This results in simple examples of profinite bounded distributive lattices that are not isomorphic to the profinite completion of any bounded distributive lattice. We also show that each profinite Boolean algebra is isomorphic to the profinite completion of some Boolean algebra. It is still an open question whether each profinite Heyting algebra is isomorphic to the profinite completion of some Heyting algebra.

APA, Harvard, Vancouver, ISO, and other styles

43

Chaudhry, Muhammad Anwar, and Hafiz Fakhar-Ud-Din. "On some classes of BCH-algebras." International Journal of Mathematics and Mathematical Sciences 25, no. 3 (2001): 205–11. http://dx.doi.org/10.1155/s0161171201003957.

Full text

Abstract:

The concept of a BCH-algebra is a generalization of the concept of a BCI-algebra. It is shown that weakly commutative BCH-algebras are weakly commutative BCI-algebras. Moreover, the concepts of weakly positive implicative and weakly implicative BCH-algebras are defined and it is shown that every weakly implicative BCH-algebra is a weakly positive implicative BCH-algebra. The weakly positive implicative BCH-algebras are characterized with the help of their self maps. Two open problems are posed.

APA, Harvard, Vancouver, ISO, and other styles

44

Tong, Jie, and Quanqin Jin. "Non-commutative Poisson Algebra Structures on the Lie Algebra $so_n\widetilde{({\Bbb C}_Q)}$." Algebra Colloquium 14, no. 03 (September 2007): 521–36. http://dx.doi.org/10.1142/s100538670700048x.

Full text

Abstract:

Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on [Formula: see text] are determined.

APA, Harvard, Vancouver, ISO, and other styles

45

Zhou, Shuyun, and Li Guo. "Rota-Baxter TD Algebra and Quinquedendriform Algebra." Algebra Colloquium 24, no. 01 (February 15, 2017): 53–74. http://dx.doi.org/10.1142/s1005386717000037.

Full text

Abstract:

A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Similar dendriform type algebras with three-part and four-part splitting of the associativity were later obtained. These structures can also be derived from actions of suitable linear operators, such as a Rota-Baxter operator or TD operator, on an associative algebra. Motivated by finding a five-part splitting of the associativity, we consider the Rota-Baxter TD (RBTD) operator, an operator combining the Rota-Baxter operator and TD operator, and coming from a recent study of Rota’s problem concerning linear operators on associative algebras. Free RBTD algebras on rooted forests are constructed. We then introduce the concept of a quinquedendriform algebra and show that its defining relations are characterized by the action of an RBTD operator, similar to the cases of dendriform and tridendriform algebras.

APA, Harvard, Vancouver, ISO, and other styles

46

Yang, Xinbing, and Xiaochun Fang. "The Tracial Class Property for Crossed Products by Finite Group Actions." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/745369.

Full text

Abstract:

We define the concept of tracial𝒞-algebra ofC*-algebras, which generalize the concept of local𝒞-algebra ofC*-algebras given by H. Osaka and N. C. Phillips. Let𝒞be any class of separable unitalC*-algebras. LetAbe an infinite dimensional simple unital tracial𝒞-algebra with the (SP)-property, and letα:G→Aut(A)be an action of a finite groupGonAwhich has the tracial Rokhlin property. ThenA ×α Gis a simple unital tracial𝒞-algebra.

APA, Harvard, Vancouver, ISO, and other styles

47

Grewcoe, Clay James, Larisa Jonke, Toni Kodžoman, and George Manolakos. "From Hopf Algebra to Braided L∞-Algebra." Universe 8, no. 4 (April 1, 2022): 222. http://dx.doi.org/10.3390/universe8040222.

Full text

Abstract:

We show that an L∞-algebra can be extended to a graded Hopf algebra with a codifferential. Then, we twist this extended L∞-algebra with a Drinfel’d twist, simultaneously twisting its modules. Taking the L∞-algebra as its own (Hopf) module, we obtain the recently proposed braided L∞-algebra. The Hopf algebra morphisms are identified with the strict L∞-morphisms, whereas the braided L∞-morphisms define a more general L∞-action of twisted L∞-algebras.

APA, Harvard, Vancouver, ISO, and other styles

48

Amini, Massoud. "Locally Compact Pro-C*-Algebras." Canadian Journal of Mathematics 56, no. 1 (February 1, 2004): 3–22. http://dx.doi.org/10.4153/cjm-2004-001-6.

Full text

Abstract:

AbstractLet X be a locally compact non-compact Hausdorff topological space. Consider the algebras C(X), Cb(X), C0(X), and C00(X) of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions on X. Of these, the second and third are C*-algebras, the fourth is a normed algebra, whereas the first is only a topological algebra (it is indeed a pro-C*- algebra). The interesting fact about these algebras is that if one of them is given, the others can be obtained using functional analysis tools. For instance, given the C*-algebra C0(X), one can get the other three algebras by C00(X) = K(C0(X)), Cb(X) = M(C0(X)), C(X) = Γ(K(C0(X))), where the right hand sides are the Pedersen ideal, the multiplier algebra, and the unbounded multiplier algebra of the Pedersen ideal of C0(X), respectively. In this article we consider the possibility of these transitions for general C*-algebras. The difficult part is to start with a pro-C*-algebra A and to construct a C*-algebra A0 such that A = Γ(K(A0)). The pro-C*-algebras for which this is possible are called locally compact and we have characterized them using a concept similar to that of an approximate identity.

APA, Harvard, Vancouver, ISO, and other styles

49

Zhou, Yanqiu, Yumeng Li, and Yunhe Sheng. "3-Lie∞-algebras and 3-Lie 2-algebras." Journal of Algebra and Its Applications 16, no. 09 (September 30, 2016): 1750171. http://dx.doi.org/10.1142/s0219498817501717.

Full text

Abstract:

In this paper, we introduce the notions of a [Formula: see text]-[Formula: see text]-algebra and a 3-Lie 2-algebra. The former is a model for a 3-Lie algebra that satisfy the fundamental identity up to all higher homotopies, and the latter is the categorification of a 3-Lie algebra. We prove that the 2-category of 2-term [Formula: see text]-[Formula: see text]-algebras is equivalent to the 2-category of 3-Lie 2-algebras. Skeletal and strict 3-Lie 2-algebras are studied in detail. A construction of a 3-Lie 2-algebra from a symplectic 3-Lie algebra is given.

APA, Harvard, Vancouver, ISO, and other styles

50

Kurniadi, Edi. "Symplectic Form yang Berkaitan Dengan Satu-form Suatu Aljabar Lie Berdimensi Rendah." Journal of Mathematics: Theory and Applications 6, no. 1 (April 5, 2024): 1–7. http://dx.doi.org/10.31605/jomta.v6i1.3096.

Full text

Abstract:

In this paper, we study symplectic form on low dimensional real Lie algebra. A symplectic form is very important in classifying of Lie algebra types. Based on their dimension and certain conditions, there are two types of Lie algebras. A lie algebra with odd dimension endowed with one-form such that is called a contact Lie algebra, while a Lie algebra whose dimension is even and it is endowed with zero index is called a Frobenius Lie algebra. The research aimed to give explicit formula of a symplectic form of low dimensional contact Lie algebras and Frobenius Lie algebras. We established that a one-form associated to simplectic form determine a type of a Lie algebra whether a contact or a Frobenius Lie algebras.To clearer the main results, we give some examples of one-form and symplectic form of Frobenius and contact Lie algebras.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!