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Von Neumann Algebras Of Strongly Connected Higher-Rank Graphs, Marcelo Laca, Nadia S. Larsen, Sergey Neshveyev, Aidan Sims, Samuel B. Webster

Faculty of Engineering and Information Sciences - Papers: Part A

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 …