Crossed products of Hom-Hopf algebras

Abstract

Let (H,?) be a Hom-Hopf algebra and (A,?) be a Hom-algebra. In this paper we will construct the Hom-crossed product (A#?H???), and prove that the extension A ? A#?H is actually a Hom-type cleft extension and vice versa. Then we will give the necessary and sufficient conditions to make (A#?H???) into a Hom-Hopf algebra. Finally we will study the lazy 2-cocycle on (H,?).

Some Results About Hom-Comodule Algebras With Hom-Hopf Module Structure

“…In [2], Blattner and Montgomery gave several characterizations of crossed products. Lu and Wang [5] generalized the results in [1] to the case of Hom-Hopf algebras. Hopf modules (see [9]) are vector spaces with both a comodule and module structure which are related in a natural way.…”

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Hom-Yang-Baxter equations and Hom-Yang-Baxter systems

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