{"paper":{"title":"Some classification results for generalized q-gaussian algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Bogdan Udrea, Marius Junge, Stephen Longfield","submitted_at":"2014-10-29T23:39:19Z","abstract_excerpt":"To any trace preserving action $\\sigma: G \\curvearrowright A$ of a countable discrete group on a finite von Neumann algebra $A$ and any orthogonal representation $\\pi:G \\to \\mathcal O(\\ell^2_{\\mathbb{R}}(G))$, we associate the generalized q-gaussian von Neumann algebra $A \\rtimes_{\\sigma} \\Gamma_q^{\\pi}(G,K)$, where $K$ is an infinite dimensional separable Hilbert space. Specializing to the cases of $\\pi$ being trivial or given by conjugation, we then prove that if $G \\curvearrowright A = L^{\\infty}(X)$, $G' \\curvearrowright B = L^{\\infty}(Y)$ are p.m.p. free ergodic rigid actions, the commuta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8199","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"}