Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2001
 arXiv:
 arXiv:math/0108126
 Bibcode:
 2001math......8126A
 Keywords:

 KTheory and Homology
 EPrint:
 Final version, to appear in "Communications in Algebra"