Alternative twisted tensor products and Cayley algebras

Details Alternative twisted tensor products and Cayley algebras Alternative twisted tensor products and Cayley algebras

2010-11-08

arxiv.org/abs/1011.1820v1

Mathematics

Rings and Algebras

13 pages; accepted for publication in Communications in Algebra

Scientific paper

We introduce what we call "alternative twisted tensor products" for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-Dickson process, the Clifford process 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 process (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.

Affiliated with

Also associated with

No associations

Rating

Alternative twisted tensor products and Cayley algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Alternative twisted tensor products and Cayley algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Alternative twisted tensor products and Cayley algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131423