Hopf algebra equivariant cyclic homology and cyclic homology of crossed product algebras

Abstract

We introduce the cylindrical module A♮H, where H is a Hopf algebra and A is a Hopf module algebra over H.We show that there exists an isomorphism between C • (A op ⋊H cop ) the cyclic module of the crossed product algebra A op ⋊ H cop , and ∆(A♮H), the cyclic module related to the diagonal of A♮H.If S, the antipode of H, is invertible it follows that C • (A ⋊ H) ≃ ∆(A op ♮H cop ).When S is invertible, we approximate HC • (A ⋊ H) by a spectral sequence and give an interpretation of E 0 , E 1 and E 2 terms of this spectral sequence.