Crossed products of Hom-Hopf algebras

shuangjian Guo


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


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