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REPRESENTATIONS OF CLIFFORD ALGEBRAS AND ITS APPLICATIONS

Susumu Ôkubo

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 $C(4,3)$.

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Key concepts: Clifford algebra, Classification of Clifford algebras, Mathematics, Spinor, Algebra over a field, Connection (principal bundle), Representation (politics), Pure mathematics