{"paper":{"title":"$*$-Freeness in Finite Tensor Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Benoit Collins, Pierre Yves Gaudreau Lamarre","submitted_at":"2016-05-01T18:26:31Z","abstract_excerpt":"In this paper, we consider the following question and variants thereof: given $\\mathbf D:=\\big(a_{1;i}\\otimes\\cdots\\otimes a_{K;i}:i\\in I\\big)$, a collection of elementary tensor non-commutative random variables in the tensor product of probability spaces $(\\mathcal A_1\\otimes\\cdots\\otimes\\mathcal A_K,\\phi_1\\otimes\\cdots\\otimes\\phi_K)$, when is $\\mathbf D$ $*$-free? (See Section 1.2 for a precise formulation of this problem.)\n  Settling whether or not freeness occurs in tensor products is a recurring problem in operator algebras, and the following two examples provide a natural motivation for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00288","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"}