On hom-algebras with surjective twisting

Details On hom-algebras with surjective twisting On hom-algebras with surjective twisting

2009-06-17

arxiv.org/abs/0906.3270v3

Mathematics

Rings and Algebras

13 pages. Final version submitted for publication

Scientific paper

A hom-associative structure is a set $A$ together with a binary operation $\star$ and a selfmap $\alpha$ such that an $\alpha$-twisted version of associativity is fulfilled. In this paper, we assume that $\alpha$ is surjective. We show that in this case, under surprisingly weak additional conditions on the multiplication, the binary operation is a twisted version of an associative operation. As an application, an earlier result by Yael Fregier and the author on weakly unital hom-algebras is recovered with a different proof. In the second section, consequences for the deformation theory of hom-algebras with surjective twisting map are discussed.

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