{"paper":{"title":"Quantum Symmetries and Strong Haagerup Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michael Brannan","submitted_at":"2010-12-30T02:56:24Z","abstract_excerpt":"In this paper, we consider families of operators $\\{x_r\\}_{r \\in \\Lambda}$ in a tracial C$^\\ast$-probability space $(\\mathcal A, \\phi)$, whose joint $\\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\\{H_n^+\\}_{n \\in \\N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\\mathcal B$ generated by $\\{x_r\\}_{r \\in \\Lambda}$, which generalizes the strong Haagerup inequalities for $\\ast$-free R-diagonal families obtained by Kemp-Speicher \\cite{KeSp}. As an application of our result, we show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0033","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"}