C*-dynamical invariants and Toeplitz algebras of graphs

2021/03/04 by Chris Bruce, Bruce, Chris, Takuya Takeishi +1
Mathematics · Physics and Astronomy · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Primary 46L30 #Secondary 82B10

paper · pdf · doi:10.48550/arxiv.2103.02816

openalex publication_date 2021/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

In recent joint work of the authors with Laca, we precisely formulated the notion of partition function in the context of C*-dynamical systems. Here, we compute the partition functions of C*-dynamical systems arising from Toeplitz algebras of graphs, and we explicitly recover graph-theoretic information in terms of C*-dynamical invariants. In addition, we compute the type for KMS states on C*-algebras of finite (reducible) graphs and prove that the extremal KMS states at critical inverse temperatures give rise to type III_λ factors. Our starting point is an independent result parameterising the partition functions of a certain class of C*-dynamical systems arising from groupoid C*-algebras in terms of β-summable orbits.

Citations

• Reconstructing directed graphs from generalised gauge actions on their Toeplitz algebras

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