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: $\RHom_A(M,M)\#H\longrightarrow \RHom_{A\#H}(M\ot H,M\ot H)$. This result is applied to $d$-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras.
Citation
Ji-Wei He. Fred Van Oystaeyen. Yinhuo Zhang. "Hopf algebra actions on differential graded algebras and applications." Bull. Belg. Math. Soc. Simon Stevin 18 (1) 99 - 111, march 2011. https://doi.org/10.36045/bbms/1299766491
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