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# The periodic cyclic homology of crossed products of finite type algebras

Brodzki, Jacek, Dave, Shantanu and Nistor, Victor (2017) The periodic cyclic homology of crossed products of finite type algebras. Advances in Mathematics, 306, 494-523.

Record type: Article

## Abstract

We study the periodic cyclic homology groups of the cross-product of a finite type algebra A by a discrete group. In case A is commutative and the group is finite, our results are complete and given in terms of the singular cohomology of the sets of fixed points. These groups identify our cyclic homology groups with the orbifold cohomology'of the underlying (algebraic) orbifold. The proof is based on a careful study of localization at fixed points and of the resulting Koszul complexes. This is achieved by extending to our class of noncommutative algebras the concept of an infinitesimal neighborhood' that plays such an important role in commutative algebra. We provide examples of Azumaya algebras for which this identification is, however, no longer valid. As an example, we discuss some affine Weyl groups.

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Accepted/In Press date: 20 October 2016
e-pub ahead of print date: 4 November 2016
Published date: 14 January 2017
Organisations: Pure Mathematics

## Identifiers

Local EPrints ID: 401819
URI: http://eprints.soton.ac.uk/id/eprint/401819
ISSN: 0001-8708
PURE UUID: 5e4a90e1-2ca0-475b-8cfb-8a786ca237b0

## Catalogue record

Date deposited: 25 Oct 2016 10:16

## Contributors

Author: Jacek Brodzki
Author: Shantanu Dave
Author: Victor Nistor