{"paper":{"title":"K-theory for the $C^*$-algebras of the solvable Baumslag-Solitar groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Alain Valette, Sanaz Pooya","submitted_at":"2016-04-19T14:54:19Z","abstract_excerpt":"We provide a new computation of the K-theory of the group $C^*$-algebra of the solvable Baumslag-Solitar group $BS(1,n)\\;(n\\neq 1)$; our computation is based on the Pimsner-Voiculescu 6-terms exact sequence, by viewing $BS(1,n)$ as a semi-direct product $\\mathbb{Z}[1/n]\\rtimes\\mathbb{Z}$. We deduce from it a new proof of the Baum-Connes conjecture with trivial coefficients for $BS(1,n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05607","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"}