Representations of Clifford Algebras and its Applications

Abstract

A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple system in terms of 8-component spinors associated with the Clifford algebras $C(0,7)$ and $C(4,3)$.

arXiv comment30 pages, UR1377

References in corpus (1)

• Triple Products and Yang-Baxter Equation (I): Octonionic and Quaternionic Triple Systems

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• A special irreducible matrix representation of the real Clifford algebra C(3,1)
• New spinor classes on the Graf-Clifford algebra
• Group Theoretical Description of Space Inversion, Time Reversal and Charge Conjugation
• A unified approach to Fierz identities
• A Symbolic Algorithm for Computation of Non-degenerate Clifford Algebra Matrix Representations