{"paper":{"title":"C*-norms for tensor products of discrete group C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Matthew Wiersma","submitted_at":"2014-06-10T18:14:20Z","abstract_excerpt":"Let $\\Gamma$ be a discrete group. We show that if $\\Gamma$ is nonamenable, then the algebraic tensor products $C^*_r(\\Gamma)\\otimes C^*_r(\\Gamma)$ and $C^*(\\Gamma)\\otimes C^*_r(\\Gamma)$ do not admit unique $C^*$-norms. Moreover, when $\\Gamma_1$ and $\\Gamma_2$ are discrete groups containing copies of noncommutative free groups, then $C^*_r(\\Gamma_1)\\otimes C^*_r(\\Gamma_2)$ and $C^*(\\Gamma_1)\\otimes C_r^*(\\Gamma_2)$ admit $2^{\\aleph_0}$ $C^*$-norms. Analogues of these results continue to hold when these familiar group $C^*$-algebras are replaced by appropriate intermediate group $C^*$-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2654","kind":"arxiv","version":2},"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"}