Publication Details

Laca, M., Larsen, N. S., Neshveyev, S., Sims, A. D. & Webster, S. B. (2015). Von Neumann algebras of strongly connected higher-rank graphs. Mathematische Annalen, 363 (1), 657-678.


We investigate the factor types of the extremal KMS states for the preferred dynamics on the Toeplitz algebra and the Cuntz-Krieger algebra of a strongly connected finite (Formula presented.)-graph. For inverse temperatures above 1, all of the extremal KMS states are of type (Formula presented.). At inverse temperature 1, there is a dichotomy: if the (Formula presented.)-graph is a simple (Formula presented.)-dimensional cycle, we obtain a finite type (Formula presented.) factor; otherwise we obtain a type III factor, whose Connes invariant we compute in terms of the spectral radii of the coordinate matrices and the degrees of cycles in the graph.

Grant Number

ARC/FT100100533, ARC/DP150101595