{"paper":{"title":"Matrix models for noncommutative algebraic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Julien Bichon, Teodor Banica","submitted_at":"2016-06-03T14:47:11Z","abstract_excerpt":"We discuss the notion of matrix model, $\\pi:C(X)\\to M_K(C(T))$, for algebraic submanifolds of the free complex sphere, $X\\subset S^{N-1}_{\\mathbb C,+}$. When $K\\in\\mathbb N$ is fixed there is a universal such model, which factorizes as $\\pi:C(X)\\to C(X^{(K)})\\subset M_K(C(T))$. We have $X^{(1)}=X_{class}$ and, under a mild assumption, inclusions $X^{(1)}\\subset X^{(2)}\\subset X^{(3)}\\subset\\ldots\\subset X$. Our main results concern $X^{(2)},X^{(3)},X^{(4)},\\ldots$, their relation with various half-classical versions of $X$, and lead to the construction of families of higher half-liberations of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01115","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"}