{"paper":{"title":"Some explicit computations and models of free products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Madhushree Basu","submitted_at":"2011-11-26T18:46:28Z","abstract_excerpt":"In this note, we first work out some `bare hands' computations of the most elementary possible free products involving $\\mathbb{C}^2 ~(=\\mathbb{C} \\oplus \\mathbb{C} $) and $M_2 ~(= M_2(\\mathbb{C}))$. Using these, we identify all free products $C \\ast D$, where $C,D$ are of the form $A_1 \\oplus A_2$ or $M_2(B)$; $A_1,A_2,B$ are finite von Neumann algebras, as is $A_1 \\oplus A_2$ with the 'uniform trace' given by $tr(a_1, a_2) = 1/2 (tr(a_1) + tr(a_2))\\}$ and $M_2(B)$ with the normalized trace given by $tr((b_{i,j}))=1/2(tr(b_{1,1}) + tr(b_{2,2}))$. Those results are then used to compute various"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6183","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"}