Hopf algebra actions on differential graded algebras and applications

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 -> RHom(A#H)(M circle times H, M circle times H). This result is applied to d-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras.