Rationally AF algebras and KMS states of Z-absorbing C*-algebras

2022/07/24 by George A. Elliott, Elliott, George A., Yasuhiko Sato +1
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.2207.11653

openalex publication_date 2022/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In order to realize all possible KMS-bundles on the Jiang-Su algebra, we introduce a class of C*-algebras which we call rationally approximately finite dimensional (RAF). Using these, we show that for a given proper simplex bundle (S, π) with a singleton π^-1(\0\) and a unital separable monotracial C*-algebra A absorbing the Jiang-Su algebra tensorially (for instance, the irrational rotation algebra), there exists a flow on A whose KMS-bundle is isomorphic to (S, π).

Related

• The admissible KMS bundles on classifiable C^*-algebras
• The bundle of KMS state spaces for flows on a unital C*-algebra
• Strongly self-absorbing C*-algebras are Z-stable
• A universal property for the Jiang-Su algebra
• Central sequence C*-algebras and tensorial absorption of the Jiang-Su algebra