On the classification of simple approximately subhomogeneous C*-algebras not necessarily of real rank zero

2003/12/02 by Cristian Ivanescu, C. Ivanescu, Ivanescu, C.
Mathematics · #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05

paper · pdf · doi:10.48550/arxiv.math/0312044

37 pages, 1 figure

openalex publication_date 2003/12/02 · arxiv created 2003/12/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their spectrum homeomorphic to the interval [0,1] or to a finite disjoint union of closed intervals. In particular, a classification of those stably AI algebras which are inductive limits of hereditary sub-C*-algebras of interval algebras is obtained. Also, the range of the invariant is calculated.

Related

• The classification ofseparable simple C*-algebras which are inductive limits of continuous-trace C*-algebraswith spectrum homeomorphic to the closed interval [0,1]
• The classification of simple separable KK-contractible C*-algebras with finite nuclear dimension
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• Reduction of the dimension of nuclear C*-algebras
• UHF slicing and classification of nuclear C*-algebras