A classification of finite simple amenable \(\mathcal{Z}\)-stable \(C^*\)-algebras. I: \(C^*\)-algebras with generalized tracial rank one

MaRDI QIDQ6600235

Guihua Gong, Huaxin Lin, Zhuang Niu

Publication date: 9 September 2024

Published in: Comptes Rendus Mathématiques de l'Académie des Sciences (Search for Journal in Brave)

zbMATH Keywords

classification of simple \(C^*\)-algebras

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) General theory of (C^*)-algebras (46L05) Classifications of (C^*)-algebras (46L35)

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Related Items (14)

Approximate equivalence of representations of AH algebras into semifinite von Neumann factors ⋮ Remarks on Villadsen algebras ⋮ A geometric Elliott invariant and noncommutative rigidity of mapping tori ⋮ Bauer simplices and the small boundary property ⋮ A topology on \(E\)-theory ⋮ \( \text{C}^*\)-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces ⋮ On classification of nonunital amenable simple \(C^*\)-algebras. IV: Stably projectionless \(C^*\)-algebras ⋮ A classification of finite simple amenable \(\mathcal{Z}\)-stable \(C^*\)-algebras. II: \(C^*\)-algebras with rational generalized tracial rank one ⋮ The bundle of KMS state spaces for flows on a unital AF C\(^*\)-algebra ⋮ K-theory and traces ⋮ Generalized tracially approximated C\(^*\)-algebras ⋮ Nuclear dimension of graph \(C^*\)-algebras with condition (K) ⋮ Radius of comparison and mean topological dimension: \( \mathbb{Z}^d\)-actions ⋮ Unitary groups, \(\boldsymbol{K}\)-theory, and traces

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