On the classification of simple amenable C*-algebras with finite decomposition rank, II

2015/07/13 by George A. Elliott, Guihua Gong, Elliott, George A. +5
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1507.03437

openalex publication_date 2015/07/13 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/28

Abstract

We prove that every unital stably finite simple amenable C^*-algebra A with finite nuclear dimension and with UCT such that every trace is quasi-diagonal has the property that A⊗ Q has generalized tracial rank at most one, where Q is the universal UHF-algebra. Consequently, A is classifiable in the sense of Elliott.

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