Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras

الأصل · EN

In this paper we construct a cylindrical module A H for an H-comodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A H is isomorphic with the cyclic module of the crossed product algebra A H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a cocylindrical module for Hopf module coalgebras and establish a similar spectral sequence to compute the cyclic cohomology of crossed product coalgebras.