K-theory and exact sequences of partial translation algebras
K-theory and exact sequences of partial translation algebras
In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context. We apply this general framework to compute the K-theory of partial translation algebras and group C*-algebras in the context of almost invariant subspaces of discrete groups. This generalises the work of Cuntz, Lance, Pimsner and Voiculescu. In particular we provide a new perspective on Pimsner’s calculation of the K-theory for a graph product of groups.
partial translation algebras, group C*-algebras, C*-algebra extensions, K-theory, almost invariant sets, pimsner–voiculescu sequence, hilbert modules, bass–serre theory
287-323
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
19 March 2015
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Brodzki, Jacek, Niblo, Graham A. and Wright, Nick
(2015)
K-theory and exact sequences of partial translation algebras.
Advances in Mathematics, 273, .
(doi:10.1016/j.aim.2014.12.023).
Abstract
In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context. We apply this general framework to compute the K-theory of partial translation algebras and group C*-algebras in the context of almost invariant subspaces of discrete groups. This generalises the work of Cuntz, Lance, Pimsner and Voiculescu. In particular we provide a new perspective on Pimsner’s calculation of the K-theory for a graph product of groups.
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Submitted date: 26 April 2013
Accepted/In Press date: 24 December 2014
e-pub ahead of print date: 19 January 2015
Published date: 19 March 2015
Keywords:
partial translation algebras, group C*-algebras, C*-algebra extensions, K-theory, almost invariant sets, pimsner–voiculescu sequence, hilbert modules, bass–serre theory
Organisations:
Pure Mathematics
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Local EPrints ID: 373659
URI: http://eprints.soton.ac.uk/id/eprint/373659
ISSN: 0001-8708
PURE UUID: b4093864-b2d1-4e57-8084-f16160165343
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Date deposited: 27 Jan 2015 14:49
Last modified: 15 Mar 2024 03:22
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