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Artículos de revistas sobre el tema "Clifford algebras"

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Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 1 de agosto de 2024

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1

Aragón, G., J. L. Aragón y M. A. Rodríguez. "Clifford algebras and geometric algebra". Advances in Applied Clifford Algebras 7, n.º 2 (diciembre de 1997): 91–102. http://dx.doi.org/10.1007/bf03041220.

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2

DA ROCHA, ROLDÃO, ALEX E. BERNARDINI y JAYME VAZ. "κ-DEFORMED POINCARÉ ALGEBRAS AND QUANTUM CLIFFORD–HOPF ALGEBRAS". International Journal of Geometric Methods in Modern Physics 07, n.º 05 (agosto de 2010): 821–36. http://dx.doi.org/10.1142/s0219887810004567.

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The Minkowski space–time quantum Clifford algebra structure associated with the conformal group and the Clifford–Hopf alternative κ-deformed quantum Poincaré algebra is investigated in the Atiyah–Bott–Shapiro mod 8 theorem context. The resulting algebra is equivalent to the deformed anti-de Sitter algebra [Formula: see text], when the associated Clifford–Hopf algebra is taken into account, together with the associated quantum Clifford algebra and a (not braided) deformation of the periodicity Atiyah–Bott–Shapiro theorem.

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3

Değırmencı, N. y Ş. Karapazar. "Explicit isomorphisms of real Clifford algebras". International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–13. http://dx.doi.org/10.1155/ijmms/2006/78613.

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It is well known that the Clifford algebraClp,qassociated to a nondegenerate quadratic form onℝn (n=p+q)is isomorphic to a matrix algebraK(m)or direct sumK(m)⊕K(m)of matrix algebras, whereK=ℝ,ℂ,ℍ. On the other hand, there are no explicit expressions for these isomorphisms in literature. In this work, we give a method for the explicit construction of these isomorphisms.

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4

Ceballos, Johan. "About the Dirichlet Boundary Value Problem using Clifford Algebras". JOURNAL OF ADVANCES IN MATHEMATICS 15 (12 de noviembre de 2018): 8098–119. http://dx.doi.org/10.24297/jam.v15i0.7795.

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This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre.

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5

Lewis, D. W. "A note on Clifford algebras and central division algebras with involution". Glasgow Mathematical Journal 26, n.º 2 (julio de 1985): 171–76. http://dx.doi.org/10.1017/s0017089500005954.

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In this note we consider the question as to which central division algebras occur as the Clifford algebra of a quadratic form over a field. Non-commutative ones other than quaternion division algebras can occur and it is also the case that there are certain central division algebras D which, while not themselves occurring as a Clifford algebra, are such that some matrix ring over D does occur as a Clifford algebra. We also consider the further question as to which involutions on the division algebra can occur as one of two natural involutions on the Clifford algebra.

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6

Hasiewicz, Z., K. Thielemans y W. Troost. "Superconformal algebras and Clifford algebras". Journal of Mathematical Physics 31, n.º 3 (marzo de 1990): 744–56. http://dx.doi.org/10.1063/1.528802.

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7

GLITIA, DANA DEBORA. "Modular G-graded algebras and G-algebras of endomorphisms". Carpathian Journal of Mathematics 30, n.º 3 (2014): 301–8. http://dx.doi.org/10.37193/cjm.2014.03.14.

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We study Clifford Theory and field extensions for strongly group-graded algebras. In [Turull, A., Clifford theory and endoisomorphisms, J. Algebra 371 (2012), 510–520] and [Turull, A., Endoisomorphisms yield mo-dule and character correspondences, J. Algebra 394 (2013), 7–50] the author introduced the notion of endoisomorphism showing that there is a natural connection between it and Clifford Theory of finite group algebras. An endoisomorphism is an isomorphism between G-algebras of endomorphisms, where G is a finite group. We consider here endoisomorphisms between modules over strongly G-graded algebras. An endoisomorphism induces equivalences of categories with some good compatibility properties (see Theorem ?? and Theorem ?? below).

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8

Cassidy, Thomas y Michaela Vancliff. "Skew Clifford algebras". Journal of Pure and Applied Algebra 223, n.º 12 (diciembre de 2019): 5091–105. http://dx.doi.org/10.1016/j.jpaa.2019.03.012.

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9

CASTRO, CARLOS. "POLYVECTOR SUPER-POINCARÉ ALGEBRAS, M, F THEORY ALGEBRAS AND GENERALIZED SUPERSYMMETRY IN CLIFFORD-SPACES". International Journal of Modern Physics A 21, n.º 10 (20 de abril de 2006): 2149–72. http://dx.doi.org/10.1142/s0217751x06028916.

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Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic supersymmetric point-particle action in Clifford-space backgrounds. The relativistic supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the Clifford-space background's polyvector-valued coordinates. To finalize, the Polyvector super-Poincaré and M, F theory superalgebras, in D = 11, 12 dimensions, respectively, are discussed followed by our final analysis of the novel Clifford-superspace realizations of generalized supersymmetries in Clifford spaces.

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10

Kuznetsov, Sergey P., Vladimir V. Mochalov y Vasiliy P. Chuev. "ALGORITHM FOR FINDING THE INVERSE ELEMENTS AND SOLUTION OF THE SILVESTER EQUATION IN THE CLIFFORD ALGEBRAS R4,0, R1,3, R5,0". Vestnik Chuvashskogo universiteta, n.º 4 (26 de diciembre de 2023): 109–19. http://dx.doi.org/10.47026/1810-1909-2023-4-109-119.

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The purpose of the work is to find an algorithm for finding inverse elements in the Clifford algebras R4,0, R1,3, R5,0 and to solve the nonlinear Sylvester equation . Materials and methods. Using the basic conjugation operations in Clifford algebras, finding an algorithm for finding inverse elements. Application of this algorithm to solve the Sylvester equation. Results of the work. In Clifford algebras R4,0, R1,3, R5,0, which have a great application in physics, a method for finding inverse elements and equations for finding zero divisors were found. The found algorithm is used to solve the Sylvester equation. For Clifford algebras of even dimension R4,0, R1,3 an algorithm for finding inverse elements is given. Finding inverse elements is closely related to the concept of zero divisors in these algebras. The inverse element method is used to solve the Sylvester equation, using even conjugation, reverse conjugation and Clifford conjugation. For the odd Clifford algebra R5,0, a conjugation is found that can be used to apply the algorithm for finding the inverse element. The method of finding the inverse element is used to solve the Sylvester equation, which, in particular, is used to ensure the robustness of the piezodrive using the controlled relative interval method. Findings. An algorithm for finding inverse elements is constructed and the Sylvester equation is solved in the Clifford algebras R4,0, R1,3, R5,0.

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11

Sobczyk, Garret. "Structure of factor algebras and clifford algebra". Linear Algebra and its Applications 241-243 (julio de 1996): 803–10. http://dx.doi.org/10.1016/0024-3795(95)00604-4.

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12

SCHOTT, RENÉ y G. STACEY STAPLES. "OPERATOR CALCULUS AND INVERTIBLE CLIFFORD APPELL SYSTEMS: THEORY AND APPLICATION TO THE n-PARTICLE FERMION ALGEBRA". Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, n.º 01 (marzo de 2013): 1350007. http://dx.doi.org/10.1142/s0219025713500070.

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Motivated by evolution equations on Clifford algebras and illustrated with the n-particle fermion algebra, a theory of invertible left- and right-Appell systems is developed for Clifford algebras of an arbitrary quadratic form. This work extends and clarifies the authors' earlier work on Clifford Appell systems, operator calculus, and operator homology/cohomology. A direct connection is also shown between blade factorization algorithms and the construction of Appell systems in these algebras.

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13

Nafari, Manizheh y Michaela Vancliff. "Graded Skew Clifford Algebras That Are Twists of Graded Clifford Algebras". Communications in Algebra 43, n.º 2 (22 de octubre de 2014): 719–25. http://dx.doi.org/10.1080/00927872.2013.847949.

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14

Carey, A. L. y D. E. Evans. "Algebras almost commuting with Clifford algebras". Journal of Functional Analysis 88, n.º 2 (febrero de 1990): 279–98. http://dx.doi.org/10.1016/0022-1236(90)90107-v.

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15

Floerchinger, Stefan. "Real Clifford Algebras and Their Spinors for Relativistic Fermions". Universe 7, n.º 6 (28 de mayo de 2021): 168. http://dx.doi.org/10.3390/universe7060168.

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Real Clifford algebras for arbitrary numbers of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real, complex or quaternionic type. Spinors are defined as elements of minimal or quasi-minimal left ideals within the Clifford algebra and as representations of the pin and spin groups. Two types of Dirac adjoint spinors are introduced carefully. The relationship between mathematical structures and applications to describe relativistic fermions is emphasized throughout.

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16

Shirokov, Dmitry. "Development of the Method of Averaging in Clifford Geometric Algebras". Mathematics 11, n.º 16 (21 de agosto de 2023): 3607. http://dx.doi.org/10.3390/math11163607.

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We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras. These operators generalize Reynolds operators from the representation theory of finite groups. We prove a number of new properties of these operators. Using the generalized Reynolds operators, we give a complete proof of the generalization of Pauli’s theorem to the case of Clifford algebras of arbitrary dimension. The results can be used in geometry, physics, engineering, computer science, and other applications.

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17

Colombo, Fabrizio, David Kimsey, Stefano Pinton y Irene Sabadini. "Slice monogenic functions of a Clifford variable via the 𝑆-functional calculus". Proceedings of the American Mathematical Society, Series B 8, n.º 23 (6 de octubre de 2021): 281–96. http://dx.doi.org/10.1090/bproc/94.

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In this paper we define a new function theory of slice monogenic functions of a Clifford variable using the S S -functional calculus for Clifford numbers. Previous attempts of such a function theory were obstructed by the fact that Clifford algebras, of sufficiently high order, have zero divisors. The fact that Clifford algebras have zero divisors does not pose any difficulty whatsoever with respect to our approach. The new class of functions introduced in this paper will be called the class of slice monogenic Clifford functions to stress the fact that they are defined on open sets of the Clifford algebra R n \mathbb {R}_n . The methodology can be generalized, for example, to handle the case of noncommuting matrix variables.

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18

Timorin, V. A. "Circles and Clifford Algebras". Functional Analysis and Its Applications 38, n.º 1 (enero de 2004): 45–51. http://dx.doi.org/10.1023/b:faia.0000024867.02438.e3.

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19

El-Agawany, M. "Meson and Clifford algebras". Chaos, Solitons & Fractals 14, n.º 1 (julio de 2002): 159–62. http://dx.doi.org/10.1016/s0960-0779(01)00209-0.

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20

Witherspoon, Sarah J. "Clifford correspondence for algebras". Journal of Algebra 256, n.º 2 (octubre de 2002): 518–30. http://dx.doi.org/10.1016/s0021-8693(02)00109-6.

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21

Gordienko, A. S. "Identities on Clifford algebras". Siberian Mathematical Journal 49, n.º 1 (enero de 2008): 48–52. http://dx.doi.org/10.1007/s11202-008-0005-0.

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22

Diarra, Bertin. "p-adic Clifford algebras". Annales mathématiques Blaise Pascal 1, n.º 1 (1994): 85–103. http://dx.doi.org/10.5802/ambp.7.

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23

Rohr, Rudolf Philippe. "Transgression and Clifford algebras". Annales de l’institut Fourier 59, n.º 4 (2009): 1337–58. http://dx.doi.org/10.5802/aif.2466.

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24

Pandzic, Pavle. "Coproducts for Clifford algebras". Glasnik Matematicki 39, n.º 2 (15 de diciembre de 2004): 207–11. http://dx.doi.org/10.3336/gm.39.2.02.

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25

Abłamowicz, R., B. Fauser, K. Podlaski y J. Rembieliński. "Idempotents of Clifford Algebras". Czechoslovak Journal of Physics 53, n.º 11 (noviembre de 2003): 949–54. http://dx.doi.org/10.1023/b:cjop.0000010517.40303.67.

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26

Robinson, P. L. "Clifford algebras and isotropes". Glasgow Mathematical Journal 29, n.º 2 (julio de 1987): 249–57. http://dx.doi.org/10.1017/s001708950000690x.

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Isotropes play a distinguished rôle in the algebra of spinors. LetVbe an even-dimensional real vector space equipped with an inner productBof arbitrary signature. An isotrope of(V, B)is a subspace of the complexificationVcon whichBcis identically zero. Denote by ρ the spin representation of the complex Clifford algebraC(Vc, Bc) on a spaceSof spinors.

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27

Schott, René y G. Stacey Staples. "Partitions and Clifford algebras". European Journal of Combinatorics 29, n.º 5 (julio de 2008): 1133–38. http://dx.doi.org/10.1016/j.ejc.2007.07.003.

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28

Quéguiner-Mathieu, Anne y Jean-Pierre Tignol. "Discriminant and Clifford algebras". Mathematische Zeitschrift 240, n.º 2 (1 de junio de 2002): 345–84. http://dx.doi.org/10.1007/s002090100385.

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29

Heckenberger, I. y A. Schüler. "ON FRT– CLIFFORD ALGEBRAS". Advances in Applied Clifford Algebras 10, n.º 2 (septiembre de 2000): 267–96. http://dx.doi.org/10.1007/s00006-000-0008-9.

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30

de Traubenberg, Michel Rausch. "Clifford Algebras in Physics". Advances in Applied Clifford Algebras 19, n.º 3-4 (29 de octubre de 2009): 869–908. http://dx.doi.org/10.1007/s00006-009-0191-2.

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31

Trindade, Marco A. S., Sergio Floquet y J. David M. Vianna. "Clifford algebras, algebraic spinors, quantum information and applications". Modern Physics Letters A 35, n.º 29 (30 de julio de 2020): 2050239. http://dx.doi.org/10.1142/s0217732320502399.

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We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored in connection with states of qubits. Supersymmetry and M-superalgebra are also analyzed with our formalism. Specifically we use extensively the algebras [Formula: see text] and [Formula: see text] as well as tensor products of Clifford algebras.

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32

Haile, Darrell y Steven Tesser. "On Azumaya algebras arising from Clifford algebras". Journal of Algebra 116, n.º 2 (agosto de 1988): 372–84. http://dx.doi.org/10.1016/0021-8693(88)90224-4.

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33

Li, Li, Chunyan Wang y Xiufeng Du. "Clifford Algebra Realization of Certain Infinite-dimensional Lie Algebras". Algebra Colloquium 18, n.º 01 (marzo de 2011): 105–20. http://dx.doi.org/10.1142/s1005386711000058.

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We give a Clifford algebra realization of a certain family of infinite-dimensional Lie algebras, inspired by a result of Berman, Gao and Tan. Furthermore, we relate this realization with vertex superalgebras and quasi modules.

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34

Gu, Ying-Qiu. "A Note on the Representation of Clifford Algebras". Journal of Geometry and Symmetry in Physics 62 (2021): 29–52. http://dx.doi.org/10.7546/jgsp-62-2021-29-52.

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In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $\Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time corresponds to the simplest and best case. Besides, the relation between the curvilinear coordinate frame and the local orthonormal basis in the curved space-time is discussed in detail, the covariant derivatives of the spinor and tensors are derived, and the connection of the orthogonal basis in tangent space is calculated. These results are helpful for both theoretical analysis and practical calculation. The basis matrices are the faithful representation of Clifford algebras in any $p+q$ dimensional Minkowski space-time or Riemann space, and the Clifford calculus converts the complicated relations in geometry and physics into simple and concise algebraic operations. Clifford numbers over any number field $\mathbb{F}$ expressed by this matrix basis form a well-defined $2^n$ dimensional hypercomplex number system. Therefore, we can expect that Clifford algebras will complete a large synthesis in science.

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35

Duncan, John y A. L. T. Paterson. "C*-algebras of Clifford semigroups". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 111, n.º 1-2 (1989): 129–45. http://dx.doi.org/10.1017/s0308210500025075.

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SynopsisWe investigate algebras associated with a (discrete) Clifford semigroup S =∪ {Ge: e ∈ E{. We show that the representation theory for S is determined by an enveloping Clifford semigroup UC(S) =∪ {Gx: x ∈ X} where X is the filter completion of the semilattice E. We describe the representation theory in terms of both disintegration theory and sheaf theory.

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36

GRESNIGT, N. G., P. F. RENAUD y P. H. BUTLER. "THE STABILIZED POINCARE–HEISENBERG ALGEBRA: A CLIFFORD ALGEBRA VIEWPOINT". International Journal of Modern Physics D 16, n.º 09 (septiembre de 2007): 1519–29. http://dx.doi.org/10.1142/s0218271807010857.

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The stabilized Poincare–Heisenberg algebra (SPHA) is a Lie algebra of quantum relativistic kinematics generated by fifteen generators. It is obtained from imposing stability conditions after combining the Lie algebras of quantum mechanics and relativity. In this paper, we show how the sixteen-dimensional real Clifford algebras Cℓ(1,3) and Cℓ(3,1) can both be used to generate the SPHA. The Clifford algebra path to the SPHA avoids the traditional stability considerations. It is conceptually easier and more straightforward to work with a Clifford algebra. The Clifford algebra path suggests that the next evolutionary step toward a theory of physics at the interface of GR and QM might be to depart from working in spacetime and instead to work in spacetime–momentum.

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37

Dinh, Doan Cong. "Monogenic functions taking values in generalized Clifford algebras". Ukrains’kyi Matematychnyi Zhurnal 73, n.º 11 (23 de noviembre de 2021): 1483–91. http://dx.doi.org/10.37863/umzh.v73i11.1033.

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UDC 512.579Generalized Clifford algebras are constructed by various methods and have some applications in mathematics and physics.In this paper we introduce a new type of generalized Clifford algebra such that all components of a monogenic functionare solutions of an elliptic partial differential equation. One of our aims is to cover more partial differential equations inframework of Clifford analysis. We shall prove some Cauchy integral representation formulae for monogenic functions inthose cases.

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38

Li, Haisheng, Shaobin Tan y Qing Wang. "A certain clifford-like algebra and quantum vertex algebras". Israel Journal of Mathematics 216, n.º 1 (octubre de 2016): 441–70. http://dx.doi.org/10.1007/s11856-016-1416-4.

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39

Fauser, Bertfried. "Hecke algebra representations within Clifford geometric algebras of multivectors". Journal of Physics A: Mathematical and General 32, n.º 10 (1 de enero de 1999): 1919–36. http://dx.doi.org/10.1088/0305-4470/32/10/010.

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40

Pervova, Ekaterina. "Diffeological Clifford algebras and pseudo-bundles of Clifford modules". Linear and Multilinear Algebra 67, n.º 9 (15 de mayo de 2018): 1785–828. http://dx.doi.org/10.1080/03081087.2018.1472202.

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41

Shah, Firdous A., Aajaz A. Teali y Mawardi Bahri. "Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras". Journal of Mathematics 2022 (2 de septiembre de 2022): 1–21. http://dx.doi.org/10.1155/2022/7848503.

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The shearlet transform is a promising and powerful time-frequency tool for analyzing nonstationary signals. In this article, we introduce a novel integral transform coined as the Clifford-valued shearlet transform on Cl(p,q) algebras which is designed to represent Clifford-valued signals at different scales, locations, and orientations. We investigated the fundamental properties of the Clifford-valued shearlet transform including Parseval’s formula, isometry, inversion formula, and characterization of range using the machinery of Clifford Fourier transforms. Moreover, we derived the pointwise convergence and homogeneous approximation properties for the proposed transform. We culminated our investigation by deriving several uncertainty principles such as the Heisenberg–Pauli–Weyl uncertainty inequality, Pitt’s inequality, and logarithmic and local-type uncertainty inequalities for the Clifford-valued shearlet transform.

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42

Albuquerque, Helena y Shahn Majid. "Clifford algebras obtained by twisting of group algebras". Journal of Pure and Applied Algebra 171, n.º 2-3 (junio de 2002): 133–48. http://dx.doi.org/10.1016/s0022-4049(01)00124-4.

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43

Hasiewicz, Z., A. K. Kwaśniewski y P. Morawiec. "On parallelizable spheres, division algebras and Clifford algebras". Reports on Mathematical Physics 23, n.º 2 (abril de 1986): 161–68. http://dx.doi.org/10.1016/0034-4877(86)90018-2.

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44

Hüttenbach, Hans Detlef. "Analytic functions for Clifford algebras". International Journal of Mathematical Analysis 15, n.º 1 (2021): 61–69. http://dx.doi.org/10.12988/ijma.2021.912140.

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45

Marchuk, N. G. "Classification of Extended Clifford Algebras". Russian Mathematics 62, n.º 11 (noviembre de 2018): 23–27. http://dx.doi.org/10.3103/s1066369x18110038.

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46

Huyen, Nguyen Thi y Doan Thanh Son. "Some Representations of Clifford Algebras". International Journal of Mathematics Trends and Technology 68, n.º 4 (25 de abril de 2022): 72–80. http://dx.doi.org/10.14445/22315373/ijmtt-v68i4p511.

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47

Chantladze, Tamaz, Nodar Kandelaki y Douglas Ugulava. "On Some Matrix Clifford Algebras". gmj 12, n.º 1 (marzo de 2005): 15–25. http://dx.doi.org/10.1515/gmj.2005.15.

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Abstract A sequence of matrices 𝑈1, 𝑈2, . . . , 𝑈𝑚 is constructed, which satisfies the conditions 𝑈𝑖𝑈𝑗 = – 𝑈𝑗𝑈𝑖 (𝑖 ≢ 𝑗), . These matrices are used to construct representations of a Clifford algebra for special quadratic forms.

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48

Ahlfors, Lars V. y Pertti Lounesto. "Some remarks on clifford algebras". Complex Variables, Theory and Application: An International Journal 12, n.º 1-4 (octubre de 1989): 201–9. http://dx.doi.org/10.1080/17476938908814365.

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49

Abłamowicz, Rafał. "Matrix Exponential via Clifford Algebras". Journal of Nonlinear Mathematical Physics 5, n.º 3 (enero de 1998): 294–313. http://dx.doi.org/10.2991/jnmp.1998.5.3.5.

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50

Botman, David M. y William P. Joyce. "Geometric equivalence of Clifford algebras". Journal of Mathematical Physics 47, n.º 12 (diciembre de 2006): 123504. http://dx.doi.org/10.1063/1.2375037.

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