HOPF ALGEBRA ACTIONS ON DIFFERENTIAL GRADED ALGEBRAS AND APPLICATIONS

Let H be a finite dimensional semisimple Hopf algebra, A a differ- ential 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: RHomA(M,M)#H −! RHomA#H(M H,M H). This result is applied to d-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras.