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K-theory and exact sequences of partial translation algebras

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
0001-8708
287-323
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
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, 287-323. (doi:10.1016/j.aim.2014.12.023).

Record type: Article

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

Identifiers

Local EPrints ID: 373659
URI: http://eprints.soton.ac.uk/id/eprint/373659
ISSN: 0001-8708
PURE UUID: b4093864-b2d1-4e57-8084-f16160165343
ORCID for Graham A. Niblo: ORCID iD orcid.org/0000-0003-0648-7027
ORCID for Nick Wright: ORCID iD orcid.org/0000-0003-4884-2576

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Date deposited: 27 Jan 2015 14:49
Last modified: 20 Jul 2019 01:21

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Contributors

Author: Jacek Brodzki
Author: Graham A. Niblo ORCID iD
Author: Nick Wright ORCID iD

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