C*-dynamical invariants and Toeplitz algebras of graphs

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${}_{\lambda }$ 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 $\beta$-summable orbits.

40 pages

References in corpus (5)

• Partial actions and KMS states on relative graph $C^{\ast }$-algebras
• von Neuman algebras of strongly connected higher-rank graphs
• Partition functions as C*-dynamical invariants and actions of congruence monoids
• Reconstructing directed graphs from generalised gauge actions on their Toeplitz algebras
• (Non)exotic completions of the group algebras of isotropy groups

Cited by in corpus (1)

• Limits of KMS states on Toeplitz algebras of finite graphs