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Journal articles on the topic 'Clifford algebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Aragón, G., J. L. Aragón, and M. A. Rodríguez. "Clifford algebras and geometric algebra." Advances in Applied Clifford Algebras 7, no. 2 (1997): 91–102. http://dx.doi.org/10.1007/bf03041220.

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2

Ceballos, Johan. "About the Dirichlet Boundary Value Problem using Clifford Algebras." JOURNAL OF ADVANCES IN MATHEMATICS 15 (November 12, 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

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3

DA ROCHA, ROLDÃO, ALEX E. BERNARDINI та JAYME VAZ. "κ-DEFORMED POINCARÉ ALGEBRAS AND QUANTUM CLIFFORD–HOPF ALGEBRAS". International Journal of Geometric Methods in Modern Physics 07, № 05 (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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4

Değırmencı, N., and 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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5

Lewis, D. W. "A note on Clifford algebras and central division algebras with involution." Glasgow Mathematical Journal 26, no. 2 (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, and W. Troost. "Superconformal algebras and Clifford algebras." Journal of Mathematical Physics 31, no. 3 (1990): 744–56. http://dx.doi.org/10.1063/1.528802.

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7

Kuznetsov, Sergey P., Vladimir V. Mochalov, and 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, no. 4 (December 26, 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 algori

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8

GLITIA, DANA DEBORA. "Modular G-graded algebras and G-algebras of endomorphisms." Carpathian Journal of Mathematics 30, no. 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-grade

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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, no. 10 (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

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10

SCHOTT, RENÉ, and 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, no. 01 (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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11

Cassidy, Thomas, and Michaela Vancliff. "Skew Clifford algebras." Journal of Pure and Applied Algebra 223, no. 12 (2019): 5091–105. http://dx.doi.org/10.1016/j.jpaa.2019.03.012.

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12

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

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13

Floerchinger, Stefan. "Real Clifford Algebras and Their Spinors for Relativistic Fermions." Universe 7, no. 6 (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 thro

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14

Shirokov, Dmitry. "Development of the Method of Averaging in Clifford Geometric Algebras." Mathematics 11, no. 16 (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

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15

Prodanov, Dimiter. "Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras." Mathematics 13, no. 7 (2025): 1106. https://doi.org/10.3390/math13071106.

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Clifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomials, inverses, and minimal polynomials of general multivectors residing in a non-degenerate Clifford algebra of an arbitrary dimension. The characteristic polynomial and inverse computation are achieved by a translation of the classical Faddeev–LeVerrier–Souriau (FVS) algorithm in the language of Clifford algebra. The demonstrated algorithms are implemented in

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16

Nafari, Manizheh, and Michaela Vancliff. "Graded Skew Clifford Algebras That Are Twists of Graded Clifford Algebras." Communications in Algebra 43, no. 2 (2014): 719–25. http://dx.doi.org/10.1080/00927872.2013.847949.

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17

Carey, A. L., and D. E. Evans. "Algebras almost commuting with Clifford algebras." Journal of Functional Analysis 88, no. 2 (1990): 279–98. http://dx.doi.org/10.1016/0022-1236(90)90107-v.

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18

Colombo, Fabrizio, David Kimsey, Stefano Pinton та Irene Sabadini. "Slice monogenic functions of a Clifford variable via the 𝑆-functional calculus". Proceedings of the American Mathematical Society, Series B 8, № 23 (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 Clif

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19

Trindade, Marco A. S., Sergio Floquet, and J. David M. Vianna. "Clifford algebras, algebraic spinors, quantum information and applications." Modern Physics Letters A 35, no. 29 (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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20

Timorin, V. A. "Circles and Clifford Algebras." Functional Analysis and Its Applications 38, no. 1 (2004): 45–51. http://dx.doi.org/10.1023/b:faia.0000024867.02438.e3.

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21

El-Agawany, M. "Meson and Clifford algebras." Chaos, Solitons & Fractals 14, no. 1 (2002): 159–62. http://dx.doi.org/10.1016/s0960-0779(01)00209-0.

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22

Witherspoon, Sarah J. "Clifford correspondence for algebras." Journal of Algebra 256, no. 2 (2002): 518–30. http://dx.doi.org/10.1016/s0021-8693(02)00109-6.

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23

Gordienko, A. S. "Identities on Clifford algebras." Siberian Mathematical Journal 49, no. 1 (2008): 48–52. http://dx.doi.org/10.1007/s11202-008-0005-0.

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24

Diarra, Bertin. "p-adic Clifford algebras." Annales mathématiques Blaise Pascal 1, no. 1 (1994): 85–103. http://dx.doi.org/10.5802/ambp.7.

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25

Rohr, Rudolf Philippe. "Transgression and Clifford algebras." Annales de l’institut Fourier 59, no. 4 (2009): 1337–58. http://dx.doi.org/10.5802/aif.2466.

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26

Pandzic, Pavle. "Coproducts for Clifford algebras." Glasnik Matematicki 39, no. 2 (2004): 207–11. http://dx.doi.org/10.3336/gm.39.2.02.

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27

Abłamowicz, R., B. Fauser, K. Podlaski, and J. Rembieliński. "Idempotents of Clifford Algebras." Czechoslovak Journal of Physics 53, no. 11 (2003): 949–54. http://dx.doi.org/10.1023/b:cjop.0000010517.40303.67.

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28

Robinson, P. L. "Clifford algebras and isotropes." Glasgow Mathematical Journal 29, no. 2 (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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29

Schott, René, and G. Stacey Staples. "Partitions and Clifford algebras." European Journal of Combinatorics 29, no. 5 (2008): 1133–38. http://dx.doi.org/10.1016/j.ejc.2007.07.003.

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30

Quéguiner-Mathieu, Anne, and Jean-Pierre Tignol. "Discriminant and Clifford algebras." Mathematische Zeitschrift 240, no. 2 (2002): 345–84. http://dx.doi.org/10.1007/s002090100385.

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31

Heckenberger, I., and A. Schüler. "ON FRT– CLIFFORD ALGEBRAS." Advances in Applied Clifford Algebras 10, no. 2 (2000): 267–96. http://dx.doi.org/10.1007/s00006-000-0008-9.

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32

de Traubenberg, Michel Rausch. "Clifford Algebras in Physics." Advances in Applied Clifford Algebras 19, no. 3-4 (2009): 869–908. http://dx.doi.org/10.1007/s00006-009-0191-2.

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33

Li, Li, Chunyan Wang, and Xiufeng Du. "Clifford Algebra Realization of Certain Infinite-dimensional Lie Algebras." Algebra Colloquium 18, no. 01 (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

Haile, Darrell, and Steven Tesser. "On Azumaya algebras arising from Clifford algebras." Journal of Algebra 116, no. 2 (1988): 372–84. http://dx.doi.org/10.1016/0021-8693(88)90224-4.

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35

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

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36

Duncan, John, and A. L. T. Paterson. "C*-algebras of Clifford semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 111, no. 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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37

GRESNIGT, N. G., P. F. RENAUD, and P. H. BUTLER. "THE STABILIZED POINCARE–HEISENBERG ALGEBRA: A CLIFFORD ALGEBRA VIEWPOINT." International Journal of Modern Physics D 16, no. 09 (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 t

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38

Dinh, Doan Cong. "Monogenic functions taking values in generalized Clifford algebras." Ukrains’kyi Matematychnyi Zhurnal 73, no. 11 (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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39

Trindade, Marco A. S., Sergio Floquet, and J. David M. Vianna. "A general formulation based on algebraic spinors for the quantum computation." International Journal of Geometric Methods in Modern Physics 17, no. 14 (2020): 2050206. http://dx.doi.org/10.1142/s0219887820502060.

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In this work, we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially, we present a general formulation through elements of minimal left ideals in tensor products of Clifford algebras. Posteriorly, we perform some applications in quantum computation: qubits, entangled states, quantum gates, representations of the braid group, quantum teleportation, Majorana operators and supersymmetry. Finally, we discuss advantages compared to standard Hilbert space formulation.

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40

DA ROCHA, R., and J. VAZ. "CONFORMAL STRUCTURES AND TWISTORS IN THE PARAVECTOR MODEL OF SPACETIME." International Journal of Geometric Methods in Modern Physics 04, no. 04 (2007): 547–76. http://dx.doi.org/10.1142/s0219887807002193.

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Some properties of the Clifford algebras [Formula: see text] and [Formula: see text] are presented, and three isomorphisms between the Dirac–Clifford algebra [Formula: see text] and [Formula: see text] are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU(2,2) and the group $pin+(2,4) is also investigated, in the light of a suitable isomorphism between [Formula: see text] and [Formula: see text]. After reviewing the conformal spacetime structure, conformal maps are des

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41

Shah, Firdous A., Aajaz A. Teali, and Mawardi Bahri. "Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras." Journal of Mathematics 2022 (September 2, 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

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42

Li, Haisheng, Shaobin Tan, and Qing Wang. "A certain clifford-like algebra and quantum vertex algebras." Israel Journal of Mathematics 216, no. 1 (2016): 441–70. http://dx.doi.org/10.1007/s11856-016-1416-4.

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43

Fauser, Bertfried. "Hecke algebra representations within Clifford geometric algebras of multivectors." Journal of Physics A: Mathematical and General 32, no. 10 (1999): 1919–36. http://dx.doi.org/10.1088/0305-4470/32/10/010.

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44

Pervova, Ekaterina. "Diffeological Clifford algebras and pseudo-bundles of Clifford modules." Linear and Multilinear Algebra 67, no. 9 (2018): 1785–828. http://dx.doi.org/10.1080/03081087.2018.1472202.

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45

Albuquerque, Helena, and Shahn Majid. "Clifford algebras obtained by twisting of group algebras." Journal of Pure and Applied Algebra 171, no. 2-3 (2002): 133–48. http://dx.doi.org/10.1016/s0022-4049(01)00124-4.

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46

Hasiewicz, Z., A. K. Kwaśniewski, and P. Morawiec. "On parallelizable spheres, division algebras and Clifford algebras." Reports on Mathematical Physics 23, no. 2 (1986): 161–68. http://dx.doi.org/10.1016/0034-4877(86)90018-2.

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47

Hüttenbach, Hans Detlef. "Analytic functions for Clifford algebras." International Journal of Mathematical Analysis 15, no. 1 (2021): 61–69. http://dx.doi.org/10.12988/ijma.2021.912140.

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48

Marchuk, N. G. "Classification of Extended Clifford Algebras." Russian Mathematics 62, no. 11 (2018): 23–27. http://dx.doi.org/10.3103/s1066369x18110038.

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49

Huyen, Nguyen Thi, and Doan Thanh Son. "Some Representations of Clifford Algebras." International Journal of Mathematics Trends and Technology 68, no. 4 (2022): 72–80. http://dx.doi.org/10.14445/22315373/ijmtt-v68i4p511.

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50

Chantladze, Tamaz, Nodar Kandelaki, and Douglas Ugulava. "On Some Matrix Clifford Algebras." gmj 12, no. 1 (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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