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arXiv · 1509.01518

Crossed product Hom-Hopf algebras and lazy 2-cocycle

Daowei Lu·Shuangjian Guo
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Abstract

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 $(A\#_σH,\bø\a)$, and prove that the extension $A\subseteq A\#_σH$ is actually a Hom-type cleft extension and vice versa. Then we will give the necessary and sufficient conditions to make $(A\#_σH,\bø\a)$ a Hom-Hopf algebra. Finally we will study the lazy 2-cocycle on $(H,\a)$.

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Daowei Lu, Shuangjian Guo. 2020-04-07. Crossed product Hom-Hopf algebras and lazy 2-cocycle. https://arxiv.org/abs/1509.01518

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