von Neuman algebras of strongly connected higher-rank graphs
Operator Algebras
2021-06-10 v2
Abstract
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 -graph. For inverse temperatures above 1, all of the extremal KMS states are of type I. At inverse temperature 1, there is a dichotomy: if the -graph is a simple -dimensional cycle, we obtain a finite type I 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.
Keywords
Cite
@article{arxiv.1409.6481,
title = {von Neuman algebras of strongly connected higher-rank graphs},
author = {Marcelo Laca and Nadia S. Larsen and Sergey Neshveyev and Aidan Sims and Samuel B. G. Webster},
journal= {arXiv preprint arXiv:1409.6481},
year = {2021}
}
Comments
16 pages; 1 picture prepared using TikZ. Version 2: this version to appear in Math. Ann