{"paper":{"title":"On generalized universal irrational rotation algebras and the operator $u+v$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Chunlan Jiang, Feng Xu, Huaxin Lin, Junsheng Fang","submitted_at":"2012-10-17T15:34:27Z","abstract_excerpt":"We introduce a class of generalized universal irrational rotation $C^*$-algebras $A_{\\theta,\\gamma}=C^*(x,w)$ which is characterized by the relations $w^*w=ww^*=1$, $x^*x=\\gamma(w)$, $xx^*=\\gamma(e^{-2\\pi i\\theta}w)$, and $xw=e^{-2\\pi i\\theta}wx$, where $\\theta$ is an irrational number and $\\gamma(z)\\in C(\\mathbb{T})$ is a positive function. We characterize tracial linear functionals, simplicity, and $K$-groups of $A_{\\theta,\\gamma}$ in terms of zero points of $\\gamma(z)$. We show that if $A_{\\theta,\\gamma}$ is simple then $A_{\\theta,\\gamma}$ is an $A{\\mathbb T}$-algebra of real rank zero. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4771","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"}