On hom-algebras with surjective twisting

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.