Title: Alternative twisted tensor products and Cayley algebras
Abstract:We introduce what we call twisted tensor for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-Dickson process, the Clifford and the twist...We introduce what we call twisted tensor for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-Dickson process, the Clifford and the twisted tensor product of two associative algebras, one of them being commutative. We show that some very basic facts concerning the Cayley-Dickson (the equivalence between the two different formulations of it and the lifting of the involution) are particular cases of general results about alternative twisted tensor products of algebras. As a class of examples of alternative twisted tensor products, we introduce a tripling process for an algebra endowed with a strong involution, containing the Cayley-Dickson doubling as a subalgebra and sharing some of its basic properties.Read More
Publication Year: 2010
Publication Date: 2010-11-08
Language: en
Type: preprint
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