Work

C*-dynamical invariants and Toeplitz algebras of graphs

Year: 2024

Type: article

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.

Source: Journal of Operator Theory

DOI: 10.7900/jot.2022oct26.2394

Authors: Chris Bruce, Takuya Takeishi

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Victoria, European Commission, Natural Sciences and Engineering Research Council of Canada, Japan Society for the Promotion of Science

Awards: G434337789, G521056402, G5768258237, G6625337319, Investigation of operator algebras associated to number fields

OpenAlex ID: W4287284746

FWCI: 0.651

Cites:

Cited by: 2

Related to: 10