Classification of inductive limits of 1-dimensional NCCW complexes

2010/07/12 by Leonel Robert, Robert, Leonel · 6 citations
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1007.1964

arxiv created 2012/08/24 · arxiv updated 2012/08/28

Abstract

A classification result is obtained for the C*-algebras that are (stably isomorphic to) inductive limits of 1-dimensional noncommutative CW complexes with trivial K₁-group. The classifying functor Cu is defined in terms of the Cuntz semigroup of the unitization of the algebra. For the simple C*-algebras covered by the classification, Cu reduces to the ordered K₀-group, the cone of traces, and the pairing between them. As an application of the classification, it is shown that the crossed products by a quasi-free action O₂\rtimes_λℝ are all isomorphic for a dense set of positive irrational numbers λ.

Cited by

• Selfless reduced free products and graph products of C^∗-algebras
• Generic classification of the quasi-free flows on the Cuntz algebra O₂
• A homotopy rigidity theorem for Z₀-stable C^∗-algebras
• C^*-diagonal of inductive limit of 1-dimensional NCCW complexes
• Self-adjoint operators in Z-stable C^*-algebras with prescribed spectral data
• Selfless reduced free product C^*-algebras

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