{"paper":{"title":"Quantum automorphisms of twisted group algebras and free hypergeometric laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Julien Bichon, Stephen Curran, Teodor Banica","submitted_at":"2010-02-16T20:42:47Z","abstract_excerpt":"We prove that we have an isomorphism of type $A_{aut}(\\mathbb C_\\sigma[G])\\simeq A_{aut}(\\mathbb C[G])^\\sigma$, for any finite group $G$, and any 2-cocycle $\\sigma$ on $G$. In the particular case $G=\\mathbb Z_n^2$, this leads to a Haar-measure preserving identification between the subalgebra of $A_o(n)$ generated by the variables $u_{ij}^2$, and the subalgebra of $A_s(n^2)$ generated by the variables $X_{ij}=\\sum_{a,b=1}^np_{ia,jb}$. Since $u_{ij}$ is \"free hyperspherical\" and $X_{ij}$ is \"free hypergeometric\", we obtain in this way a new free probability formula, which at $n=\\infty$ correspon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3146","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"}