{"paper":{"title":"A model theoretic Rieffel's theorem of quantum 2-torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Boris Zilber, Masanori Itai","submitted_at":"2017-08-08T19:23:44Z","abstract_excerpt":"We defined a notion of quantum 2-torus $T_\\theta$ in \"Masanori Itai and Boris Zilber, Notes on a model theory of quantum 2-torus $T_q^2$ for generic $q$, arXiv:1503.06045v1 [mathLO]\" and studied its model theoretic property. In this note we associate quantum 2-tori $T_\\theta$ with the structure over ${\\mathbb C}_\\theta = ({\\mathbb C}, +, \\cdot, y = x^\\theta),$ where $\\theta \\in {\\mathbb R} \\setminus {\\mathbb Q}$, and introduce the notion of geometric isomorphisms between such quantum 2-tori.\n  We show that this notion is closely connected with the fundamental notion of Morita equivalence of no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02615","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"}