Cayley-dickson algebras and alternative loop algebras

Abstract

In this paper we establish a relationship between alternative loop algebras and Cayley-Dickson algebras: any Cayley-Dickson algebra is a quotient algebra of an alternative loop algebra. Thus we give a new way of representing a Cayley-Dickson algebra. As an application, a result of Luiz G. X. de Barros is generalized.

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Notes on contributors

Yongxin Zhou