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The periodic cyclic homology of crossed products of finite type algebras

The periodic cyclic homology of crossed products of finite type algebras
The periodic cyclic homology of crossed products of finite type algebras
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 ? is finite, our results are complete and given in terms of the singular cohomology of the strata of fixed points. These groups identify our cyclic homology groups with the \dlp orbifold cohomology\drp\ of the underlying (algebraic) orbifold. The proof is based on a careful study of localization at fixed points and of the resulting Koszul complexes. We provide examples of Azumaya algebras for which this identification is, however, no longer valid. As an example, we discuss some affine Weyl groups.
1-25
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Dave, Shantanu
61d050c3-7410-48b5-93ed-1ac017702e1f
Nistor, Victor
c9f95327-cc97-4d9a-a8fb-3c89e3d84bdf
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Dave, Shantanu
61d050c3-7410-48b5-93ed-1ac017702e1f
Nistor, Victor
c9f95327-cc97-4d9a-a8fb-3c89e3d84bdf

Brodzki, Jacek, Dave, Shantanu and Nistor, Victor (2015) The periodic cyclic homology of crossed products of finite type algebras. Author's Original, 1-25. (Submitted)

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 ? is finite, our results are complete and given in terms of the singular cohomology of the strata of fixed points. These groups identify our cyclic homology groups with the \dlp orbifold cohomology\drp\ of the underlying (algebraic) orbifold. The proof is based on a careful study of localization at fixed points and of the resulting Koszul complexes. We provide examples of Azumaya algebras for which this identification is, however, no longer valid.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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Submitted date: 2 September 2015
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 389380
URI: https://eprints.soton.ac.uk/id/eprint/389380
PURE UUID: f81fae16-9570-4b46-985f-4206b21042b3

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Date deposited: 07 Mar 2016 12:14
Last modified: 05 Oct 2018 12:08

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Contributors

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

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