C*-dynamical invariants and Toeplitz algebras of graphs

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.