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The Structure of the Clifford Algebra
Advances in Applied Clifford Algebras, 2009This lecture deals with the presentation of general properties of Clifford algebra and in particular Clifford algebras for Euclidean or pseudo Euclidean spaces or complex regular spaces.
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Clifford Algebras and Clifford Modules
1993We study bundles over a point, recalling the definition of the Clifford algebra Cl(V, q) of a real vector space V of dimension m equipped with a positive definite inner product q; the ℤ2-grading of Clifford algebras is shown, followed by an introduction of complex representations of Clifford algebras and the concept of complex Cl(V, q)-modules and of ...
Bernhelm Booß-Bavnbek +1 more
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Identities on Clifford algebras
Siberian Mathematical Journal, 2008Summary: We obtain some estimates of the codimensions and PI-exponents of identities on the Clifford algebras associated to a quadratic form of a given rank, find a hook where the cocharacters of Clifford algebras lie, exhibit an identity that holds on the Clifford algebras of a given rank, and describe the multilinear identities of minimal degree for ...
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Roots of algebraic equations and Clifford algebra
Advances in Applied Clifford Algebras, 1999The author investigates roots of real polynomials inside the real two-dimensional Clifford algebra with generator \(\varepsilon\), \(\varepsilon^2=1\), calling the elements of this algebra hyperbolic. The corresponding numbers of real and hyperbolic roots of a polynomial are calculated.
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Division Algebras, Clifford Algebras, Periodicity
Advances in Applied Clifford Algebras, 2018Periodicities in Clifford algebra theory of orders \(2,4,\) and \(8\) are well known. Starting from a result from lattice theory, in which a \(24\)-dimensional Leech lattice can be represented in the \(3\)-dimensional space with octonion components, the main goal of this paper is to prove that, by exploiting the octonion algebra, in Clifford algebra ...
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Clifford Bundles and Clifford Algebras
2004In view of General Relativity, it is necessary to study physical fields, including solutions of the Dirac equation, in curved spacetimes. It is generally believed that the study of Riemannian (positive definite) metrics (infinitesimal distance functions) will ultimately be relevant to the more directly physical problem of Lorentz signature metrics, via
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The Algebraic Theory of Spinors and Clifford Algebras
1996This volume is the first in a projected series devoted to the mathematical and philosophical works of the late Claude Chevalley. It covers the main contributions by the author to the theory of spinors. Since its appearance in 1954, "The Algebraic Theory of Spinors" has been a much sought after reference.
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States of the Clifford Algebra
The Annals of Mathematics, 1964Shale, D., Stinespring, W. F.
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On Clifford Algebras and Their Representations
The Annals of Mathematics, 1948openaire +1 more source