{"paper":{"title":"C*-algebras of Toeplitz type associated with algebraic number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.OA","authors_text":"Christopher Deninger, Joachim Cuntz, Marcelo Laca","submitted_at":"2011-05-26T17:06:27Z","abstract_excerpt":"We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\\cT[R]$. It is an extension of the ring C*-algebra $\\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to $\\cA[R]$, it is functorial under homomorphisms of rings. It can also be defined using the left regular representation of the $ax+b$-semigroup $R\\rtimes R^\\times$ on $\\ell^2 (R\\rtimes R^\\times)$.\n  The algebra $\\cT[R]$ carries a natural one-parameter automorphism group $(\\sigma_t)_{t\\in\\Rz}$. We determine its KMS-structure. The technical difficulties that we encount"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5352","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"}