Relevant bibliographies by topics / Clifford algebras

Academic literature on the topic 'Clifford algebras'

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Published: 4 June 2021
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Journal articles on the topic "Clifford algebras"

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

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DA ROCHA, ROLDÃO, ALEX E. BERNARDINI, and JAYME VAZ. "κ-DEFORMED POINCARÉ ALGEBRAS AND QUANTUM CLIFFORD–HOPF ALGEBRAS." International Journal of Geometric Methods in Modern Physics 07, no. 05 (August 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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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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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 solve an initial value problem related to a fibre.
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Lewis, D. W. "A note on Clifford algebras and central division algebras with involution." Glasgow Mathematical Journal 26, no. 2 (July 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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Hasiewicz, Z., K. Thielemans, and W. Troost. "Superconformal algebras and Clifford algebras." Journal of Mathematical Physics 31, no. 3 (March 1990): 744–56. http://dx.doi.org/10.1063/1.528802.

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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-graded algebras. An endoisomorphism induces equivalences of categories with some good compatibility properties (see Theorem ?? and Theorem ?? below).
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Cassidy, Thomas, and Michaela Vancliff. "Skew Clifford algebras." Journal of Pure and Applied Algebra 223, no. 12 (December 2019): 5091–105. http://dx.doi.org/10.1016/j.jpaa.2019.03.012.

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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 (April 20, 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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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 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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Dissertations / Theses on the topic "Clifford algebras"

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Han, Gang. "Clifford algebras associated with symmetric pairs /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20HAN.

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Araujo, Martinho da Costa. "Construção de algebras reais de Clifford." reponame:Repositório Institucional da UFSC, 1988. http://repositorio.ufsc.br/xmlui/handle/123456789/75476.

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Dissertação (mestrado) - Universidade Federal de Santa Catarina. Centro de Ciencias Fisicas e Matematicas
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O objetivo anunciado no título desta tese é realizado do seguinte modo: No capítulo I selecionamos definições de estruturas algébricas e de álgebra linear que usaremos nos capítulos posteriores. No capítulo II introduzimos a noção de álgebra de clifford. Estabelecemos a sua unicidade (a menos de isomorfismo) e determinamos a sua dimensão. No capítulo III tratamos da existência das álgebras de Clifford por meio de uma construção matricial explícita e formulamos uma série de critérios e teoremas que reduzem esta construção aos casos em que o espaço ortogonal é de dimensão menor que 5. Finalmente, no capítulo IV aplicamos os resultados obtidos na construção do recobrimento do grupo Spin(n) pelo grupo SO(n) e na construção da sequência de Radon-Hurwitz-Eckman.
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Wilmot, Gregory Paul. "The structure of Clifford algebra." Title page, contents and abstract only, 1988. http://web4.library.adelaide.edu.au/theses/09SM/09smw738.pdf.

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Hoefel, Eduardo Outeiral Correa. "Teorias de Gauge e algebras de Clifford." [s.n.], 2002. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307234.

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Orientador: Jayme Vaz Jr
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Nesta dissertação apresentamos uma descrição do formalismo matemático das teorias de gauge introduzindo os conceitos de grupos e álgebras de Lie, fibrados principais, conexões e curvatura. Em seguida introduzimos as álgebras de Clifford e os spinors, tais conceitos são utilizados no capítulo final onde apresenta-se algllmas de suas aplicações em teorias de gauge. Uma aplicação é dada pelas formas diferenciais assumindo valores em uma álgebra de Clifford: mostra-se como as formas de conexão e curvatura são dadas por formas a valores em álegebras de bivetores, estas últimas são as álgebras de Lie dos grupos Spin. Outra aplicação consiste em mostrar, usando o Teorema de Periodicidade das álgebras de Clifford, como algumas transformações conformes do espaço-tempo são dadas pela ação do grupo $pin(2,4) sobre paravetores ]R + ]R4,1. Finalizamos mostrando a construção de monopolos e instantons através do teorema de inversão para spinors de Pauli e Dirac, vistos como elementos de sub-álgebras pares de álgebras de Clifford, e a estreita relação deste teorema com as fibrações de Hopf, ilustrando a relação existente entre Topologia e Física
Abstract: This dissertation begins with a description of the mathematical formulation of gauge theories, introducing the concepts of Lie groups and Lie algebras, principal bundles, connection and curvature. Then, Clifford algebras and spinors are introduced. The final chapter presents some applications of Clifford algebras in gauge theories. The first application is given by Clifford algebra valued differential forms: we shown how the connection and curvature 2-forms are given by bivector algebra valued forms, bivector algebras are the Lie algebras of spin groups. Another application consist of showing, through the Periodicity Theorem of Clifford algebras, how some conformal transformations of the space-time are given by the action of the $pin(2,4) group over the paravectors R+ R4,1. ln the last application, the construction of monopoles and instantons is presented through the lnversion Theorem for Pauli and Dirac spinors, considered as elements of the even sub-algebra of the Clifford algebra. The close relationship between this theorem and the Hopf fibrations is emphasized, ilustrating the link between Topology and Physics
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Severi, Claudio. "Clifford algebras and spin groups, with physical applications." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18387/.

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In questo lavoro viene esposta la teoria delle algebre di Clifford e dei gruppi di Spin, con attenzione alle applicazioni fisiche, in particolare l'equazione di Dirac per particelle quantistiche con spin 1/2. I primi due capitoli sono dedicati ad una descrizione generale delle algebre di Clifford reali e complesse, che vengono costruite e classificate. Il terzo capitolo è dedicato ai gruppi di Spin ed alle loro algebre di Lie. Gli ultimi due capitoli illustrano un'applicazione fisica: viene esposta la teoria quantistica dello spin e del momento angolare, e si deriva l'equazione di Dirac con un principio variazionale. Dopo una discussione delle proprietà generiche di questa equazione, si dimostra che descrive accuratamente la struttura fine dello spettro dell'atomo di idrogeno.
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Wylie, Dave. "Factoring Blades and Versors in Euclidean Clifford Algebras." Thesis, Southern Illinois University at Edwardsville, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1564083.

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This thesis examines different methods of factoring elements of Clifford Algebras, specifically, Cℓn,0. Blades are factored using Fontijne's algorithm and other techniques. Versors are factored using Perwass's algorithm. Writing an element as a sum of blades, which are then factored, can make it more efficient to store or transmit that element. To evaluate the usefulness of expressing a given element of Cℓ n,0 this way, the number of scalars required to express that element is compared between factored and expanded forms.

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Buchholz, Sven [Verfasser]. "A Theory of Neural Computation with Clifford Algebras / Sven Buchholz." Kiel : Universitätsbibliothek Kiel, 2005. http://d-nb.info/1080317147/34.

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Doran, Christopher John Leslie. "Geometric algebra and its application to mathematical physics." Thesis, University of Cambridge, 1994. https://www.repository.cam.ac.uk/handle/1810/251691.

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Clifford algebras have been studied for many years and their algebraic properties are well known. In particular, all Clifford algebras have been classified as matrix algebras over one of the three division algebras. But Clifford Algebras are far more interesting than this classification suggests; they provide the algebraic basis for a unified language for physics and mathematics which offers many advantages over current techniques. This language is called geometric algebra - the name originally chosen by Clifford for his algebra - and this thesis is an investigation into the properties and applications of Clifford's geometric algebra. The work falls into three broad categories: - The formal development of geometric algebra has been patchy and a number of important subjects have not yet been treated within its framework. A principle feature of this thesis is the development of a number of new algebraic techniques which serve to broaden the field of applicability of geometric algebra. Of particular interest are an extension of the geometric algebra of spacetime (the spacetime algebra) to incorporate multiparticle quantum states, and the development of a multivector calculus for handling differentiation with respect to a linear function. - A central contention of this thesis is that geometric algebra provides the natural language in which to formulate a wide range of subjects from modern mathematical physics. To support this contention, reformulations of Grassmann calculus, Lie algebra theory, spinor algebra and Lagrangian field theory are developed. In each case it is argued that the geometric algebra formulation is computationally more efficient than standard approaches, and that it provides many novel insights. - The ultimate goal of a reformulation is to point the way to new mathematics and physics, and three promising directions are developed. The first is a new approach to relativistic multiparticle quantum mechanics. The second deals with classical models for quantum spin-I/2. The third details an approach to gravity based on gauge fields acting in a fiat spacetime. The Dirac equation forms the basis of this gauge theory, and the resultant theory is shown to differ from general relativity in a number of its features and predictions.
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Resende, Adriana Souza. "Introdução elementar às álgebras Clifford 'CL IND.2' 'CL IND. 3'." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306698.

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Orientador: Waldyr Alves Rodrigues Junior
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatistica e Computação Cientifica
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Resumo: O presente trabalho tem a intenção de apresentar por intermédio de uma linguagem unificada alguns conceitos de cálculo vetorial, álgebra linear (matrizes e transformações lineares) e também algumas idéias elementares sobre os grupos de rotações em duas e três dimensões e seus grupos de recobrimento, que geralmente são tratados como "fragmentos" em várias modalidades de cursos no ensino superior. Acreditamos portanto que nosso texto possas ser útil para alunos dos cursos de graduação dos cursos de Engenharia, Física, Matemática e interessados em Matemática em geral. A linguagem unificada à que nos referimos acima é obtida com a introdução do conceitos das álgebras geométricas (ou de Clifford) onde, como veremos, é possível fornecer uma formulação algébrica elegante aos conceitos de vetores, planos e volumes orientados e definir para tais objetos o produto escalar, os produtos contraídos à esquerda e à direita, o produto exterior (associado, como veremos, em casos particulares ao produto vetorial) e finalmente o produto geométrico (Clifford), o que permite o uso desses conceitos para a solução de inúmeros problemas de geometria analítica no R ² e no R ³. Procuramos ilustrar todos estes conceitos com vários exemplos e exercícios com graus variáveis de dificuldades. Nossa apresentação é bem próxima àquela do livro de Lounesto, e de fato muitas seções são traduções (eventualmente seguidas de comentários) de seções daquele livro. Contudo, em muitos lugares, acreditamos que nossa apresentação esclarece e completa as correspondentes do livro de Lounesto
Abstract: This paper aims to present using an unified language a few concepts of vector calculus, linear algebra (matrices and linear transformations) and also some basic ideas about the groups of rotations in two and three dimensions and their covering group, which generally are treated as "fragments" in various types of courses in higher education. We believe therefore that our text should be useful to students of undergraduate courses like Engineering, Physics, Mathematics and people interested in Mathematics in general. The unified language that we refer to above is obtained by introducing the concept of geometric (or Clifford) algebra where, as we shall see, it is possible to give an elegant algebraic formulation to the concepts of vectors, oriented planes and oriented volumes, and to define to those objects the scalar product, the right and left contracted products, the exterior product (associated, as we shall see, in particular cases to the vector product) and finally the geometric (Clifford) product, and moreover, to use those concepts to solve may problems of analytic geometry in R ² and R ³. We illustrated all those concepts with several examples and exercises with variable degrees of difficulties. Our presentation is nearly the one in Lounesto's book, and in fact some sections are no more than translations (eventually with commentaries) from sections of that book. However, in many places, we believe that our presentation clarify nd completement the corresponding ones in Lounesto's book
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Rocha, Junior Roldão da. "Spinors e twistors no modelo paravetorial : uma formulação via algebras de Clifford." [s.n.], 2001. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307233.

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Orientador: Jayme Vaz Junior
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Nesta dissertação o formalismo dos spinors e twistors de Penrose são formulados em termos das álgebras de Clifi'ord. Para tal utilizamos o modelo paravetorial do espaço-tempo, onde um vetor do espaço-tempo é escrito em termos da soma de escalares e vetores da álgebra de Cli:fford do espaço euclideano tridimensional. Com isso construímos um formalismo que utiliza a menor estrutura algébrica capaz de descrever teorias físicas relativísticas, como as teorias eletromagnética e de Dirac. Os spinors são definidos algebricamente como elementos de um ideal lateral mínimal da álgebra de Clifi'ord. Utilizamos o teorema de periodicidade (1,1) das álgebras de Clifi'ord para descrever de maneira linear, em termos da complexificação da álgebra de Clifi'ord do espaço-tempo, as transformações conformes desse espaço-tempo. Os twistors aparecem como uma classe particular de spinors algébricos. Consideramos ainda algumas possíveis generalizações
Abstract: In this dissertation the Penrose theory of spinors and twistors is formulated from the point of view of the Clifi'ord algebras. We use the paravector model of spacetime, where a spacetime vector is written as a sum of scalars and vectors of the Clifi'ord algebra associated with the three-dimensional euclidean space. From this we construct a formalism that uses the least algebraic structure that describes relativistic physical theories, such as the electromagnetic and the Dirac ones. Spinors are defined algebraically as elements of a minimallateral ideal of a Cli:fford algebra. We use the modulo (1,1) periodicity theorem of Clifi'ord algebras to describe the conformal transformations as linear transformations, using the method of complexmcation of the spacetime Clifi'ord algebra. Twistors are defined as a particular class of algebraic spinors. We consider some possible generalizations
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Books on the topic "Clifford algebras"

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Kondrat'ev, Gennadiy. Clifford Geometric Algebra. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1832489.

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The monograph is devoted to the fundamental aspects of geometric algebra and closely related issues. The category of Clifford algebras is considered as the conjugate category of vector spaces with a quadratic form. Possible constructions in this category and internal algebraic operations of an algebra with a geometric interpretation are studied. An application to the differential geometry of a Euclidean manifold based on a shape tensor is included. We consider products, coproducts and tensor products in the category of associative algebras with application to the decomposition of Clifford algebras into simple components. Spinors are introduced. Methods of matrix representation of the Clifford algebra are studied. It may be of interest to students, postgraduates and specialists in the field of mathematics, physics and cybernetics.
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Abłamowicz, Rafał, ed. Clifford Algebras. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2.

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Klawitter, Daniel. Clifford Algebras. Wiesbaden: Springer Fachmedien Wiesbaden, 2015. http://dx.doi.org/10.1007/978-3-658-07618-4.

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Baylis, William E., ed. Clifford (Geometric) Algebras. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-4104-1.

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Artibano, Micali, ed. Quadratic mappings and Clifford algebras. Basel: Birkhäuser, 2008.

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Lounesto, Pertti. Clifford algebras and spinors. Cambridge: Cambridge University Press, 1997.

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Perwass, Christian. Geometric algebra with applications in engineering. Berlin: Springer, 2009.

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Meinrenken, Eckhard. Clifford Algebras and Lie Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Snygg, John. Clifford algebras: Computational toolfor physicists. New York: Oxford University Press, 1997.

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Crumeyrolle, Albert. Orthogonal and Symplectic Clifford Algebras. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-015-7877-6.

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Book chapters on the topic "Clifford algebras"

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Eastwood, Michael. "Algebras Like Clifford Algebras." In Clifford Algebras, 265–78. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2_17.

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Scharlau, Winfried. "Clifford Algebras." In Grundlehren der mathematischen Wissenschaften, 326–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-69971-9_9.

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Husemoller, Dale. "Clifford Algebras." In Graduate Texts in Mathematics, 151–70. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4757-2261-1_12.

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Meinrenken, Eckhard. "Clifford algebras." In Clifford Algebras and Lie Theory, 23–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36216-3_2.

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Cnops, Jan. "Clifford Algebras." In An Introduction to Dirac Operators on Manifolds, 1–24. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0065-9_1.

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Chevalley, Claude. "Clifford Algebras." In The Algebraic Theory of Spinors and Clifford Algebras, 35–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60934-3_3.

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Lam, T. Y. "Clifford algebras." In Graduate Studies in Mathematics, 103–42. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/067/05.

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Mitrea, Marius. "Clifford algebras." In Lecture Notes in Mathematics, 1–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073557.

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Hassani, Sadri. "Clifford Algebras." In Mathematical Physics, 829–57. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01195-0_27.

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Hahn, Alexander J. "The Clifford Algebra in the Theory of Algebras, Quadratic Forms, and Classical Groups." In Clifford Algebras, 305–22. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2_19.

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Conference papers on the topic "Clifford algebras"

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KRASNOV, YAKOV. "COMMUTATIVE ALGEBRAS IN CLIFFORD ANALYSIS." In Proceedings of the 3rd ISAAC Congress. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812794253_0041.

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Karmakar, Sanjay, and B. Rajan. "Multigroup-Decodable STBCs from Clifford Algebras." In 2006 IEEE Information Theory Workshop. IEEE, 2006. http://dx.doi.org/10.1109/itw.2006.322857.

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Karmakar, Sanjay, and B. Sundar Rajan. "Multigroup-Decodable STBCs from Clifford Algebras." In 2006 IEEE Information Theory Workshop. IEEE, 2006. http://dx.doi.org/10.1109/itw2.2006.323839.

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Chien, Steve, Lars Rasmussen, and Alistair Sinclair. "Clifford algebras and approximating the permanent." In the thiry-fourth annual ACM symposium. New York, New York, USA: ACM Press, 2002. http://dx.doi.org/10.1145/509907.509944.

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Gürlebeck, Klaus, Wolfgang Sprössig, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Analysis in Clifford Algebras—Some Aspects." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636713.

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Sprössig, Wolfgang, Klaus Gürlebeck, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Clifford Algebras in Mathematics and Applied Sciences." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790249.

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Furui, Sadataka. "Clifford algebras and physical and engineering sciences." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825542.

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Rajan, G. Susinder, and B. Sundar Rajan. "STBCs from Representation of Extended Clifford Algebras." In 2007 IEEE International Symposium on Information Theory. IEEE, 2007. http://dx.doi.org/10.1109/isit.2007.4557141.

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SCHOTT, RENÉ, and G. STACEY STAPLES. "CLIFFORD ALGEBRAS, RANDOM GRAPHS, AND QUANTUM RANDOM VARIABLES." In Quantum Stochastics and Information - Statistics, Filtering and Control. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812832962_0005.

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Ouyang, W., and Y. Wu. "Motion Representation and Inertial Navigation in Clifford Algebras." In 2022 DGON Inertial Sensors and Systems (ISS). IEEE, 2022. http://dx.doi.org/10.1109/iss55898.2022.9926412.

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