{"paper":{"title":"Realization of a simple higher dimensional noncommutative torus as a transformation group C*-algebra","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Benjam\\'in Itz\\'a-Ortiz, N. Christopher Phillips","submitted_at":"2005-12-01T15:51:57Z","abstract_excerpt":"Let $\\theta$ be a nondegenerate skew symmetric real $d$ by $d$ matrix, and let $A_{\\theta}$ be the corresponding simple higher dimensional noncommutative torus. Suppose that $d$ is odd, or that $d$ is greater or equal to 4 and the entries of $\\theta$ are not contained in a quadratic extension of $\\mathbb{Q}$. Then $A_{\\theta}$ is isomorphic to the transformation group C*-algebra obtained from a minimal homeomorphism of a compact connected one dimensional space locally homeomorphic to the product of the interval and the Cantor set. The proof uses classification theory of C*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512030","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"}