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Статті в журналах з теми "Noncommutative algebras"

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Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 30 січня 2023

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1

Arutyunov, A. A. "Derivation Algebra in Noncommutative Group Algebras." Proceedings of the Steklov Institute of Mathematics 308, no. 1 (January 2020): 22–34. http://dx.doi.org/10.1134/s0081543820010022.

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2

Abel, Mati, and Krzysztof Jarosz. "Noncommutative uniform algebras." Studia Mathematica 162, no. 3 (2004): 213–18. http://dx.doi.org/10.4064/sm162-3-2.

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3

Xu, Ping. "Noncommutative Poisson Algebras." American Journal of Mathematics 116, no. 1 (February 1994): 101. http://dx.doi.org/10.2307/2374983.

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4

Ferreira, Vitor O., Jairo Z. Gonçalves, and Javier Sánchez. "Free symmetric algebras in division rings generated by enveloping algebras of Lie algebras." International Journal of Algebra and Computation 25, no. 06 (September 2015): 1075–106. http://dx.doi.org/10.1142/s0218196715500319.

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For any Lie algebra L over a field, its universal enveloping algebra U(L) can be embedded in a division ring 𝔇(L) constructed by Lichtman. If U(L) is an Ore domain, 𝔇(L) coincides with its ring of fractions. It is well known that the principal involution of L, x ↦ -x, can be extended to an involution of U(L), and Cimpric proved that this involution can be extended to one on 𝔇(L). For a large class of noncommutative Lie algebras L over a field of characteristic zero, we show that 𝔇(L) contains noncommutative free algebras generated by symmetric elements with respect to (the extension of) the principal involution. This class contains all noncommutative Lie algebras such that U(L) is an Ore domain.

5

Roh, Jaiok, and Ick-Soon Chang. "Approximate Derivations with the Radical Ranges of Noncommutative Banach Algebras." Abstract and Applied Analysis 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/594075.

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We consider the derivations on noncommutative Banach algebras, and we will first study the conditions for a derivation on noncommutative Banach algebra. Then, we examine the stability of functional inequalities with a derivation. Finally, we take the derivations with the radical ranges on noncommutative Banach algebras.

6

Ercolessi, Elisa, Giovanni Landi, and Paulo Teotonio-Sobrinho. "Noncommutative Lattices and the Algebras of Their Continuous Functions." Reviews in Mathematical Physics 10, no. 04 (May 1998): 439–66. http://dx.doi.org/10.1142/s0129055x98000148.

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Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for their use in quantum physics. Posets are truly noncommutative spaces, or noncommutative lattices, since they can be realized as structure spaces of noncommutative C*-algebras. These noncommutative algebras play the same rôle as the algebra of continuous functions [Formula: see text] on a Hausdorff topological space M and can be thought of as algebras of operator valued functions on posets. In this article, we will review some mathematical results that establish a duality between finite posets and a certain class of C*-algebras. We will see that the algebras in question are all postliminal approximately finite dimensional (AF) algebras.

7

LETZTER, EDWARD S. "NONCOMMUTATIVE IMAGES OF COMMUTATIVE SPECTRA." Journal of Algebra and Its Applications 07, no. 05 (October 2008): 535–52. http://dx.doi.org/10.1142/s0219498808002941.

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We initiate a unified, axiomatic study of noncommutative algebras R whose prime spectra are, in a natural way, finite unions of commutative noetherian spectra. Our results illustrate how these commutative spectra can be functorially "sewn together" to form Spec R. In particular, we construct a bimodule-determined functor Mod Z → Mod R, for a suitable commutative noetherian ring Z, from which there follows a finite-to-one, continuous surjection Spec Z → Spec R. Algebras satisfying the given axiomatic framework include PI algebras finitely generated over fields, noetherian PI algebras, enveloping algebras of complex finite dimensional solvable Lie algebras, standard generic quantum semisimple Lie groups, quantum affine spaces, quantized Weyl algebras, and standard generic quantizations of the coordinate ring of n × n matrices. In all of these examples (except for the non-finitely-generated noetherian PI algebras), Z is finitely generated over a field, and the constructed map of spectra restricts to a surjection Max Z → Prim R.

8

Mahanta, Snigdhayan. "Noncommutative stable homotopy and stable infinity categories." Journal of Topology and Analysis 07, no. 01 (December 2, 2014): 135–65. http://dx.doi.org/10.1142/s1793525315500077.

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The noncommutative stable homotopy category NSH is a triangulated category that is the universal receptacle for triangulated homology theories on separable C*-algebras. We show that the triangulated category NSH is topological as defined by Schwede using the formalism of (stable) infinity categories. More precisely, we construct a stable presentable infinity category of noncommutative spectra and show that NSHop sits inside its homotopy category as a full triangulated subcategory, from which the above result can be deduced. We also introduce a presentable infinity category of noncommutative pointed spaces that subsumes C*-algebras and define the noncommutative stable (co)homotopy groups of such noncommutative spaces generalizing earlier definitions for separable C*-algebras. The triangulated homotopy category of noncommutative spectra admits (co)products and satisfies Brown representability. These properties enable us to analyze neatly the behavior of the noncommutative stable (co)homotopy groups with respect to certain (co)limits. Along the way we obtain infinity categorical models for some well-known bivariant homology theories like KK-theory, E-theory, and connective E-theory via suitable (co)localizations. The stable infinity category of noncommutative spectra can also be used to produce new examples of generalized (co)homology theories for noncommutative spaces.

9

Utudee, Somlak. "Tensor Products of Noncommutative Lp-Spaces." ISRN Algebra 2012 (May 14, 2012): 1–9. http://dx.doi.org/10.5402/2012/197468.

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We consider the notion of tensor product of noncommutative Lp spaces associated with finite von Neumann algebras and define the notion of tensor product of Haagerup noncommutative Lp spaces associated with σ-finite von Neumann algebras.

10

BLOHMANN, CHRISTIAN. "PERTURBATIVE SYMMETRIES ON NONCOMMUTATIVE SPACES." International Journal of Modern Physics A 19, no. 32 (December 30, 2004): 5693–706. http://dx.doi.org/10.1142/s0217751x04021238.

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Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semisimple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. The result can be used to construct invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.

11

Eriksen, Eivind, and Arvid Siqveland. "Geometry of noncommutative algebras." Banach Center Publications 93 (2011): 69–82. http://dx.doi.org/10.4064/bc93-0-6.

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12

LOPEZ, ANTONIO FERNANDEZ. "NONCOMMUTATIVE JORDAN RIESZ ALGEBRAS." Quarterly Journal of Mathematics 39, no. 1 (1988): 67–80. http://dx.doi.org/10.1093/qmath/39.1.67.

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13

Brown, Robert B., and Nora C. Hopkins. "Noncommutative matrix Jordan algebras." Transactions of the American Mathematical Society 333, no. 1 (January 1, 1992): 137–55. http://dx.doi.org/10.1090/s0002-9947-1992-1068925-4.

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14

Casas, J. M., and T. Datuashvili. "Noncommutative Leibniz–Poisson Algebras." Communications in Algebra 34, no. 7 (August 2006): 2507–30. http://dx.doi.org/10.1080/00927870600651091.

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15

Abdullaev, R., S. Egamov, and B. Iskandarov. "Isomorphisms of Noncommutative Log-algebras." Bulletin of Science and Practice, no. 12 (December 15, 2022): 43–46. http://dx.doi.org/10.33619/2414-2948/85/05.

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16

Liu, Yong Lin, and Xiaobo Cai. "Pseudo-Weak-R0Algebras." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/352381.

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A positive answer to the open problem of Iorgulescu on extending weak-R0algebras andR0-algebras to the noncommutative forms is given. We show that pseudo-weak-R0algebras are categorically isomorphic to pseudo-IMTL algebras and that pseudo-R0algebras are categorically isomorphic to pseudo-NM algebras. Some properties, the noncommutative forms of the properties in weak-R0algebras andR0-algebras, are investigated. The simplified axiom systems of pseudo-weak-R0algebras and pseudo-R0algebras are obtained.

17

Davidson, Kenneth R., and Gelu Popescu. "Noncommutative Disc Algebras for Semigroups." Canadian Journal of Mathematics 50, no. 2 (April 1, 1998): 290–311. http://dx.doi.org/10.4153/cjm-1998-015-5.

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RésuméWe study noncommutative disc algebras associated to the free product of discrete subsemigroups of ℝ+. These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely infinite. The nonself-adjoint subalgebras determine the semigroup up to isomorphism. Moreover, we establish a dilation theorem for contractive representations of these semigroups which yields a variant of the von Neumann inequality. These methods are applied to establish a solution to the truncated moment problem in this context.

18

PIONTKOVSKI, DMITRI. "ALGEBRAS ASSOCIATED TO PSEUDO-ROOTS OF NONCOMMUTATIVE POLYNOMIALS ARE KOSZUL." International Journal of Algebra and Computation 15, no. 04 (August 2005): 643–48. http://dx.doi.org/10.1142/s0218196705002396.

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Quadratic algebras associated to pseudo-roots of noncommutative polynomials have been introduced by I. Gelfand, Retakh, and Wilson in connection with studying the decompositions of noncommutative polynomials. Later they (with S. Gelfand and Serconek) showed that the Hilbert series of these algebras and their quadratic duals satisfy the necessary condition for Koszulity. It is proved in this note that these algebras are Koszul.

19

Abel, Mati. "Dense subalgebras in noncommutative Jordan topological algebras." Acta et Commentationes Universitatis Tartuensis de Mathematica 1 (December 31, 1996): 65–70. http://dx.doi.org/10.12697/acutm.1996.01.07.

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Wilansky conjectured in [12] that normed dense Q-algebras are full subalgebras of Banach algebras. Beddaa and Oudadess proved in [2] that Wilansky’s conjecture was true. They showed that k-normed Q-algebras are full subalgebras of k-Banach algebras for each k∈(0,1]. Moreover, J. Pérez, L. Rico and A. Rodríguez showed in [8], Theorem 4, that this was also true in the case of noncommutative Jordan-Banach algebras. In the present paper this problem has been studied in a more general case. It is proved that all dense Q-subalgebras of topological algebras and of noncommutative Jordan topological algebras with continuous multiplication are full subalgebras. Some equivalent conditions that a dense subalgebra would be a Q-algebra (in subspace topology) in Q-algebras and in nonassociative Jordan Q-algebras with continuous multiplication are given.

20

Hopkins, Nora C. "Noncommutative matrix jordon algebras from lie algebras." Communications in Algebra 19, no. 3 (January 1991): 767–75. http://dx.doi.org/10.1080/00927879108824168.

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21

Vasquez Campos, Brian D., and Jorge P. Zubelli. "Noncommutative Bispectral Algebras and Their Presentations." Symmetry 14, no. 10 (October 19, 2022): 2202. http://dx.doi.org/10.3390/sym14102202.

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We prove a general result on presentations of finitely generated algebras and apply it to obtain nice presentations for some noncommutative algebras arising in the matrix bispectral problem. By “nice presentation”, we mean a presentation that has as few as possible defining relations. This, in turn, has potential applications in computer algebra implementations and examples. Our results can be divided into three parts. In the first two, we consider bispectral algebras with the eigenvalue in the physical equation to be scalar-valued for 2×2 and 3×3 matrix-valued eigenfunctions. In the third part, we assume the eigenvalue in the physical equation to be matrix-valued and draw an important connection with Spin Calogero–Moser systems. In all cases, we show that these algebras are finitely presented. As a byproduct, we answer positively a conjecture of F. A. Grünbaum about these algebras.

22

Lezama, Oswaldo, and Helbert Venegas. "Center of skew PBW extensions." International Journal of Algebra and Computation 30, no. 08 (September 19, 2020): 1625–50. http://dx.doi.org/10.1142/s0218196720500575.

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In this paper we compute the center of many noncommutative algebras that can be interpreted as skew [Formula: see text] extensions. We show that, under some natural assumptions on the parameters that define the extension, either the center is trivial, or, it is of polynomial type. As an application, we provided new examples of noncommutative algebras that are cancellative.

23

Tabuada, Gonçalo, and Michel Van den Bergh. "Noncommutative motives of Azumaya algebras." Journal of the Institute of Mathematics of Jussieu 14, no. 2 (March 10, 2014): 379–403. http://dx.doi.org/10.1017/s147474801400005x.

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AbstractLet $k$ be a base commutative ring, $R$ a commutative ring of coefficients, $X$ a quasi-compact quasi-separated $k$-scheme, and $A$ a sheaf of Azumaya algebras over $X$ of rank $r$. Under the assumption that $1/r\in R$, we prove that the noncommutative motives with $R$-coefficients of $X$ and $A$ are isomorphic. As an application, we conclude that a similar isomorphism holds for every $R$-linear additive invariant. This leads to several computations. Along the way we show that, in the case of finite-dimensional algebras of finite global dimension, all additive invariants are nilinvariant.

24

Ebrahimi-Fard, Kurusch, Alexander Lundervold, and Dominique Manchon. "Noncommutative Bell polynomials, quasideterminants and incidence Hopf algebras." International Journal of Algebra and Computation 24, no. 05 (August 2014): 671–705. http://dx.doi.org/10.1142/s0218196714500283.

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Bell polynomials appear in several combinatorial constructions throughout mathematics. Perhaps most naturally in the combinatorics of set partitions, but also when studying compositions of diffeomorphisms on vector spaces and manifolds, and in the study of cumulants and moments in probability theory. We construct commutative and noncommutative Bell polynomials and explain how they give rise to Faà di Bruno Hopf algebras. We use the language of incidence Hopf algebras, and along the way provide a new description of antipodes in noncommutative incidence Hopf algebras, involving quasideterminants. We also discuss Möbius inversion in certain Hopf algebras built from Bell polynomials.

25

KAJIURA, HIROSHIGE. "NONCOMMUTATIVE HOMOTOPY ALGEBRAS ASSOCIATED WITH OPEN STRINGS." Reviews in Mathematical Physics 19, no. 01 (February 2007): 1–99. http://dx.doi.org/10.1142/s0129055x07002912.

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We discuss general properties of A∞-algebras and their applications to the theory of open strings. The properties of cyclicity for A∞-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for A∞-algebras and cyclic A∞-algebras and discuss various consequences of it. In particular, it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic A∞-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic L∞-algebras.

26

OMORI, Hideki, Yoshiaki MAEDA, Naoya MIYAZAKI, and Akira YOSHIOKA. "Noncommutative 3-sphere: A model of noncommutative contact algebras." Journal of the Mathematical Society of Japan 50, no. 4 (October 1998): 915–43. http://dx.doi.org/10.2969/jmsj/05040915.

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27

Lee, Tsiu-Kwen. "Derivations on noncommutative Banach algebras." Studia Mathematica 167, no. 2 (2005): 153–60. http://dx.doi.org/10.4064/sm167-2-3.

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28

Maszczyk, Tomasz. "Splitting Polynomials in Noncommutative Algebras." Communications in Algebra 40, no. 11 (November 2012): 4130–46. http://dx.doi.org/10.1080/00927872.2011.602780.

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29

Mori, Izuru. "Intersection multiplicity over noncommutative algebras." Journal of Algebra 252, no. 2 (June 2002): 241–57. http://dx.doi.org/10.1016/s0021-8693(02)00016-9.

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30

Dosiev, Anar. "Regularities in Noncommutative Banach Algebras." Integral Equations and Operator Theory 61, no. 3 (July 2008): 341–64. http://dx.doi.org/10.1007/s00020-008-1593-6.

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31

Pilabré, Nakelgbamba Boukary, and Akry Koulibaly. "Noncommutative duplicate and Leibniz algebras." Afrika Matematika 23, no. 1 (March 20, 2011): 99–107. http://dx.doi.org/10.1007/s13370-011-0021-2.

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32

Ruelle, David. "Noncommutative algebras for hyperbolic diffeomorphisms." Inventiones Mathematicae 93, no. 1 (February 1988): 1–13. http://dx.doi.org/10.1007/bf01393685.

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33

Tabuada, Gonçalo, and Michel Van den Bergh. "Noncommutative motives of separable algebras." Advances in Mathematics 303 (November 2016): 1122–61. http://dx.doi.org/10.1016/j.aim.2016.08.031.

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34

Emch, G. G., H. Narnhofer, W. Thirring, and G. L. Sewell. "Anosov actions on noncommutative algebras." Journal of Mathematical Physics 35, no. 11 (November 1994): 5582–99. http://dx.doi.org/10.1063/1.530766.

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35

Tapsoba, Alexis, and Nakelgbamba Boukary Pilabré. "NONCOMMUTATIVE DUPLICATE AND VINBERG ALGEBRAS." JP Journal of Algebra, Number Theory and Applications 48, no. 1 (October 20, 2020): 19–36. http://dx.doi.org/10.17654/nt048010019.

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36

Polishchuk, Alexander. "Noncommutative Proj and coherent algebras." Mathematical Research Letters 12, no. 1 (2005): 63–74. http://dx.doi.org/10.4310/mrl.2005.v12.n1.a7.

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37

Rogalski, D., S. J. Sierra, and J. T. Stafford. "Noncommutative Blowups of Elliptic Algebras." Algebras and Representation Theory 18, no. 2 (October 29, 2014): 491–529. http://dx.doi.org/10.1007/s10468-014-9506-7.

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38

Brešar, M., and J. Vukman. "Derivations of noncommutative Banach algebras." Archiv der Mathematik 59, no. 4 (October 1992): 363–70. http://dx.doi.org/10.1007/bf01197053.

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39

Arias, Alvaro, and Frédéric Latrémolière. "Classification of noncommutative domain algebras." Comptes Rendus Mathematique 350, no. 11-12 (June 2012): 609–11. http://dx.doi.org/10.1016/j.crma.2012.06.003.

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40

Crawley-Boevey, William, Pavel Etingof, and Victor Ginzburg. "Noncommutative geometry and quiver algebras." Advances in Mathematics 209, no. 1 (February 2007): 274–336. http://dx.doi.org/10.1016/j.aim.2006.05.004.

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41

Ayupov, Sh A., and K. K. Kudaybergenov. "Derivations of noncommutative Arens algebras." Functional Analysis and Its Applications 41, no. 4 (October 2007): 303–5. http://dx.doi.org/10.1007/s10688-007-0028-5.

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42

Chakraborty, Sayan. "Some remarks on $\mathrm{K}_0$ of noncommutative tori." MATHEMATICA SCANDINAVICA 126, no. 2 (May 6, 2020): 387–400. http://dx.doi.org/10.7146/math.scand.a-119699.

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Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibres are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of $\mathrm {K}_0$ for all noncommutative tori.

43

Škoda, Zoran. "Some Equivariant Constructions in Noncommutative Algebraic Geometry." gmj 16, no. 1 (March 2009): 183–202. http://dx.doi.org/10.1515/gmj.2009.183.

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Abstract We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which provide affine examples. We introduce a compatibility of monoidal actions and localizations which is a distributive law. There are satisfactory notions of equivariant objects, noncommutative fiber bundles and quotients in this setup.

44

KUDRYAVTSEVA, GANNA. "A DUALIZING OBJECT APPROACH TO NONCOMMUTATIVE STONE DUALITY." Journal of the Australian Mathematical Society 95, no. 3 (August 19, 2013): 383–403. http://dx.doi.org/10.1017/s1446788713000323.

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AbstractThe aim of the present paper is to extend the dualizing object approach to Stone duality to the noncommutative setting of skew Boolean algebras. This continues the study of noncommutative generalizations of different forms of Stone duality initiated in recent papers by Bauer and Cvetko-Vah, Lawson, Lawson and Lenz, Resende, and also the current author. In this paper we construct a series of dual adjunctions between the categories of left-handed skew Boolean algebras and Boolean spaces, the unital versions of which are induced by dualizing objects $\{ 0, 1, \ldots , n+ 1\} $, $n\geq 0$. We describe the categories of Eilenberg-Moore algebras of the monads of the adjunctions and construct easily understood noncommutative reflections of left-handed skew Boolean algebras, where the latter can be faithfully embedded (if $n\geq 1$) in a canonical way. As an application, we answer the question that arose in a recent paper by Leech and Spinks to describe the left adjoint to their ‘twisted product’ functor $\omega $.

45

Ge, Liming, and Wei Yuan. "Kadison–Singer algebras: Hyperfinite case." Proceedings of the National Academy of Sciences 107, no. 5 (January 14, 2010): 1838–43. http://dx.doi.org/10.1073/pnas.0907161107.

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A new class of operator algebras, Kadison–Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introduced to classify these algebras.

46

Baratella, Stefano. "Nonstandard Hulls of C*-Algebras and Their Applications." Mathematics 9, no. 20 (October 15, 2021): 2598. http://dx.doi.org/10.3390/math9202598.

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For the sake of providing insight into the use of nonstandard techniques à la A. Robinson and into Luxemburg’s nonstandard hull construction, we first present nonstandard proofs of some known results about C*-algebras. Then we introduce extensions of the nonstandard hull construction to noncommutative probability spaces and noncommutative stochastic processes. In the framework of internal noncommutative probability spaces, we investigate properties like freeness and convergence in distribution and their preservation by the nonstandard hull construction. We obtain a nonstandard characterization of the freeness property. Eventually we provide a nonstandard characterization of the property of equivalence for a suitable class of noncommutative stochastic processes and we study the behaviour of the latter property with respect to the nonstandard hull construction.

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LISZKA-DALECKI, JAN, and PIOTR M. SOŁTAN. "QUANTUM ISOMETRY GROUPS OF SYMMETRIC GROUPS." International Journal of Mathematics 23, no. 07 (June 27, 2012): 1250074. http://dx.doi.org/10.1142/s0129167x12500747.

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We identify the quantum isometry groups of spectral triples built on the symmetric groups with length functions arising from the nearest-neighbor transpositions as generators. It turns out that they are isomorphic to certain "doubling" of the group algebras of the respective symmetric groups. We discuss the doubling procedure in the context of regular multiplier Hopf algebras. In the last section we study the dependence of the isometry group of Sn on the choice of generators in the case n = 3. We show that two different choices of generators lead to nonisomorphic quantum isometry groups which exhaust the list of noncommutative noncocommutative semisimple Hopf algebras of dimension 12. This provides noncommutative geometric interpretation of these Hopf algebras.

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BEIL, CHARLIE. "NONNOETHERIAN HOMOTOPY DIMER ALGEBRAS AND NONCOMMUTATIVE CREPANT RESOLUTIONS." Glasgow Mathematical Journal 60, no. 2 (October 30, 2017): 447–79. http://dx.doi.org/10.1017/s0017089517000209.

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AbstractNoetherian dimer algebras form a prominent class of examples of noncommutative crepant resolutions (NCCRs). However, dimer algebras that are noetherian are quite rare, and we consider the question: how close are nonnoetherian homotopy dimer algebras to being NCCRs? To address this question, we introduce a generalization of NCCRs to nonnoetherian tiled matrix rings. We show that if a noetherian dimer algebra is obtained from a nonnoetherian homotopy dimer algebraAby contracting each arrow whose head has indegree 1, thenAis a noncommutative desingularization of its nonnoetherian centre. Furthermore, if any two arrows whose tails have indegree 1 are coprime, thenAis a nonnoetherian NCCR.

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Georgescu, George, and Laurenţiu Leuştean. "Some classes of pseudo-BL algebras." Journal of the Australian Mathematical Society 73, no. 1 (August 2002): 127–54. http://dx.doi.org/10.1017/s144678870000851x.

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AbstractPseudo-BL algebras are noncommutative generalizations of BL-algebras and they include pseudo-MV algebras, a class of structures that are categorically equivalent to l-groups with strong unit. In this paper we characterize directly indecomposable pseudo-BL algebras and we define and study different classes of these structures: local, good, perfect, peculiar, and (strongly) bipartite pseudo-BL algebras.

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BHATT, S. J., and MEETAL M. SHAH. "SECOND-ORDER NONCOMMUTATIVE DIFFERENTIAL AND LIPSCHITZ STRUCTURES DEFINED BY A CLOSED SYMMETRIC OPERATOR." Journal of the Australian Mathematical Society 100, no. 2 (November 25, 2015): 145–62. http://dx.doi.org/10.1017/s1446788715000403.

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The Banach $^{\ast }$-operator algebras, exhibiting the second-order noncommutative differential structure and the noncommutative Lipschitz structure, that are determined by the unbounded derivation and induced by a closed symmetric operator in a Hilbert space, are explored.