{"paper":{"title":"K-theory and exact sequences of partial translation algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.OA","authors_text":"Graham A. Niblo, Jacek Brodzki, Nick Wright","submitted_at":"2013-04-26T11:27:03Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7130","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}