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Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras

R. Akbarpour·M. Khalkhali
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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.

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R. Akbarpour, M. Khalkhali. 2002-12-09. Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras. https://arxiv.org/abs/math/0108126

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