On hom-algebras with surjective twisting

A hom-associative structure is a set A together with a binary operation ⋆ and a self-map α such that an α-twisted version of associativity is fulfilled. In this paper, we assume that α 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 (Fregier and Gohr [1]) 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.