On the \(K\)-theory of the \(C^\ast\)-algebra generated by the left regular representation of an Ore semigroup

DOI10.4171/JEMS/513zbMath1329.46062arXiv1201.4680OpenAlexW2962896347MaRDI QIDQ2018249

Xin Li, Joachim Cuntz, Siegfried Echterhoff

Publication date: 13 April 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.4680

zbMATH Keywords

\(K\)-theoryleft Ore semigroupreduced semigroup \(C^*\)-algebra

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) General theory of (C^*)-algebras (46L05) Algebraic numbers; rings of algebraic integers (11R04) Semigroups (20M99)

Related Items (24)

On \(K\)-theoretic invariants of semigroup \(C^\ast\)-algebras attached to number field. II ⋮ \(\mathrm C^*\)-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type ⋮ Partition functions as \(C^*\)-dynamical invariants and actions of congruence monoids ⋮ On \(K\)-theoretic invariants of semigroup \(C^*\)-algebras attached to number fields ⋮ A classification of inductive limit C∗$C^{*}$‐algebras with ideal property ⋮ Boundary quotient C*‐algebras of semigroups ⋮ Constructing number field isomorphisms from \(*\)-isomorphisms of certain crossed product \(\mathrm{C}^*\)-algebras ⋮ A boundary quotient diagram for right LCM semigroups ⋮ Operator algebras of higher rank numerical semigroups ⋮ Nuclearity of semigroup \(C^\ast\)-algebras and the connection to amenability ⋮ Symmetric monoidal noncommutative spectra, strongly self-absorbing \(C^*\)-algebras, and bivariant homology ⋮ Semigroup 𝐶*-algebras of 𝑎𝑥+𝑏-semigroups ⋮ C*-algebras from actions of congruence monoids on rings of algebraic integers ⋮ Duals of quantum semigroups with involution ⋮ On $C^*$-algebras associated to right LCM semigroups ⋮ 𝐾-theory for generalized Lamplighter groups ⋮ A going-down principle for ample groupoids and the Baum-Connes conjecture ⋮ C^*-Algebras of algebraic dynamical systems and right LCM semigroups ⋮ A new approach to recent constructions of \(C^\ast\)-algebras from modular index theory ⋮ C∗-Algebras Associated with Algebraic Actions ⋮ Semigroup C∗-Algebras ⋮ \(K\)-theory for semigroup \(C^*\)-algebras and partial crossed products ⋮ Algebraic \(K\)-theory, \(K\)-regularity, and \(\mathbb T\)-duality of \(\mathcal O_\infty\)-stable \(C^\ast\)-algebras ⋮ On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoids

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