Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras

Details Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras

2001-08-19

arxiv.org/abs/math/0108126v3

Mathematics

K-Theory and Homology

Final version, to appear in "Communications in Algebra"

Scientific paper

In this paper we construct a cylindrical module $A \natural \mathcal{H}$ for an $\mathcal{H}$-comodule algebra $A$, where the antipode of the Hopf algebra $\mathcal{H}$ is bijective. We show that the cyclic module associated to the diagonal of $A \natural \mathcal{H}$ is isomorphic with the cyclic module of the crossed product algebra $A \rtimes \mathcal{H}$. 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.

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