{"paper":{"title":"Reduced operator algebras of trace-preserving quantum automorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Michael Brannan","submitted_at":"2012-02-22T20:15:36Z","abstract_excerpt":"Let $B$ be a finite dimensional C$^\\ast$-algebra equipped with its canonical trace induced by the regular representation of $B$ on itself. In this paper, we study various properties of the trace-preserving quantum automorphism group $\\G$ of $B$. We prove that the discrete dual quantum group $\\hG$ has the property of rapid decay, the reduced von Neumann algebra $L^\\infty(\\G)$ has the Haagerup property and is solid, and that $L^\\infty(\\G)$ is (in most cases) a prime type II$_1$-factor. As applications of these and other results, we deduce the metric approximation property, exactness, simplicity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5020","kind":"arxiv","version":3},"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"}