{"paper":{"title":"Quantum symmetry groups of noncommutative tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.OA","authors_text":"Marcin Marciniak, Michal Banacki","submitted_at":"2016-06-20T18:20:49Z","abstract_excerpt":"We discuss necessary conditions for a compact quantum group to act on the algebra of noncommutative $n$-torus $\\mathbb{T}_\\theta^n$ in a filtration preserving way in the sense of Banica and Skalski. As a result, we construct a family of compact quantum groups $\\mathbb{G}_\\theta=(A_\\theta^n,\\Delta)$ such that for each $\\theta$, $\\mathbb{G}_\\theta$ is the final object in the category of all compact quantum groups acting on $\\mathbb{T}_\\theta^n$ in a filtration preserving way. We describe in details the structure of the C*-algebra $A_\\theta^n$ and provide a concrete example of its representation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06233","kind":"arxiv","version":3},"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"}