{"paper":{"title":"Isomorphism and Morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of $SL_2(\\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Christian B\\\"onicke, Hung-Chang Liao, Sayan Chakraborty, Zhuofeng He","submitted_at":"2017-11-14T10:56:08Z","abstract_excerpt":"Let $\\theta, \\theta'$ be irrational numbers and $A, B$ be matrices in $SL_2(\\mathbb{Z})$ of infinite order. We compute the $K$-theory of the crossed product $\\mathcal{A}_{\\theta}\\rtimes_A \\mathbb{Z}$ and show that $\\mathcal{A}_{\\theta} \\rtimes_A\\mathbb{Z}$ and $\\mathcal{A}_{\\theta'} \\rtimes_B \\mathbb{Z}$ are $*$-isomorphic if and only if $\\theta = \\pm\\theta' \\pmod{\\mathbb{Z}}$ and $I-A^{-1}$ is matrix equivalent to $I-B^{-1}$. Combining this result and an explicit construction of equivariant bimodules, we show that $\\mathcal{A}_{\\theta} \\rtimes_A\\mathbb{Z}$ and $\\mathcal{A}_{\\theta'} \\rtimes_B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05055","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"}