Von Neumann algebras of strongly connected higher-rank graphs

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 k -graph. For inverse temperatures above 1, all of the extremal KMS states are of type  I ∞ . At inverse temperature 1, there is...

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Bibliographic Details
Published inMathematische annalen Vol. 363; no. 1-2; pp. 657 - 678
Main Authors Laca, Marcelo, Larsen, Nadia S., Neshveyev, Sergey, Sims, Aidan, Webster, Samuel B. G.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2015
Subjects
Mathematics
Mathematics and Statistics
Primary 46L10
Secondary 46L05
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Summary: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 k -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 k -graph is a simple k -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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-015-1187-y