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 We provide examples of Azumaya algebras for which this identification is, however, no longer valid.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.
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Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Dave, Shantanu
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Nistor, Victor
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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, .
(Submitted)
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 We provide examples of Azumaya algebras for which this identification is, however, no longer valid.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.
Text
crossProd.pdf
- Author's Original
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Submitted date: 2 September 2015
Organisations:
Pure Mathematics
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Local EPrints ID: 389380
URI: http://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: 15 Mar 2024 03:11
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Author:
Shantanu Dave
Author:
Victor Nistor
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