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C*-dynamical invariants and Toeplitz algebras of graphs

Lookup NU author(s): Dr Chris BruceORCiD

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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 IIIλ 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.

Publication metadata

Author(s): Bruce C, Takeishi T

Publication type: Article

Publication status: Published

Journal: Journal of Operator Theory

Year: 2024

Volume: 92

Issue: 2

Pages: 363-411

Online publication date: 01/11/2024

Acceptance date: 15/10/2022

ISSN (print): 0379-4024

ISSN (electronic): 1841-7744

Publisher: The Theta Foundation

URL: http://dx.doi.org/10.7900/jot.2022oct26.2394

DOI: 10.7900/jot.2022oct26.2394

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