All classifiable Kirchberg algebras are \(C^\ast\)-algebras of ample groupoids

DOI10.1016/j.exmath.2019.06.001zbMath1469.46040arXiv1904.07431OpenAlexW2964180917MaRDI QIDQ2221499

Lisa Orloff Clark, James Fletcher, Astrid an Huef

Publication date: 2 February 2021

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.07431

zbMATH Keywords

groupoidKirchberg algebraclassification of \(C^\ast\)-algebrassimple purely infinite \(C^\ast\)-algebra

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Classifications of (C^*)-algebras (46L35)

Cites Work

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• Purely infinite simple \(C^\ast\)-algebras that are principal groupoid \(C^\ast\)-algebras
• Higher-rank graph \(C^*\)-algebras: an inverse semigroup and groupoid approach
• A groupoid approach to C*-algebras
• Topological methods for C*-algebras. II: Geometric resolutions and the Kuenneth formula
• The Baum-Connes conjecture for amenable foliations
• Some classifiable groupoid \(C^{*}\)-algebras with prescribed \(K\)-theory
• Classification of simple \(C^*\)-algebras of tracial topological rank zero
• Classification of certain infinite simple \(C^*\)-algebras. II
• Higher rank graph \(C^*\)-algebras
• A classification theorem for nuclear purely infinite simple \(C^*\)-algebras
• UCT-Kirchberg algebras have nuclear dimension one
• A class of \(C^{*}\)-algebras generalizing both graph algebras and homeomorphism \(C^{*}\)-algebras. IV: Pure infiniteness
• Purely infinite C^*-algebras arising from crossed products
• Properties preserved under Morita equivalence of 𝐂*-algebras
• Semiprojectivity for certain purely infinite 𝐶*-algebras
• Commutants of unitaries in UHF algebras and functorial properties of exactness.
• Purely infinite $C^*$-algebras arising from dynamical systems
• Non-cyclotomic presentations of modules and prime-order automorphisms of Kirchberg algebras
• Classification of nuclear \(C^*\)-algebras. Entropy in operator algebras

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