K-theory and exact sequences of partial translation algebras

2013/04/26 by Jacek Brodzki, Brodzki, Jacek, Graham A. Niblo +3
Mathematics · #19K35 (Secondary) #20F65 #46L80 (Primary) 46L85 #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.GR #math.KT #math.OA #msc:19K35 #msc:20F65 #msc:46L80 #msc:46L85

paper · pdf · doi:10.48550/arxiv.1304.7130

arxiv created 2013/04/26 · arxiv updated 2013/04/29

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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