Periodic cyclic homology of crossed products

TL;DR

This paper explores the periodic cyclic homology of crossed product algebras, providing a new perspective based on the Cuntz-Quillen approach and analyzing the impact of group actions on cyclic bicomplexes.

Contribution

It introduces a novel description of the periodic cyclic homology of crossed product algebras using the G-action on cyclic bicomplexes, extending previous methods.

Findings

Describes periodic cyclic homology in terms of G-actions on bicomplexes

Provides a framework connecting crossed products and cyclic homology

Offers insights into the structure of crossed product algebras

Abstract

We discuss the cyclic homology of crossed product algebras from the Cuntz-Quillen point of view. The periodic cyclic homology of a crossed product algebra $A\rtimes G$ is described in terms of the $G$-action on periodic cyclic bicomplexes of crossed products of $A$ by the cyclic subgroups of $G$ .