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arXiv · 1007.4983

Hopf algebra actions on differential graded algebras and applications

Ji-Wei He·Fred Van Oystaeyen·Yinhuo Zhang
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Abstract

Let $H$ be a finite dimensional semisimple Hopf algebra, $A$ a differential graded (dg for short) $H$-module algebra. Then the smash product algebra $A\#H$ is a dg algebra. For any dg $A\#H$-module $M$, there is a quasi-isomorphism of dg algebras: $\mathrm{RHom}_A(M,M)\#H\longrightarrow \mathrm{RHom}_{A\#H}(M\ot H,M\ot H)$. This result is applied to $d$-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras

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Ji-Wei He, Fred Van Oystaeyen, Yinhuo Zhang. 2010-07-28. Hopf algebra actions on differential graded algebras and applications. https://arxiv.org/abs/1007.4983

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