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Von Neumann algebras of strongly connected higher-rank graphs

Journal Article


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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 (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.

UOW Authors


  •   Laca, Marcelo (external author)
  •   Larsen, Nadia S. (external author)
  •   Neshveyev, Sergey (external author)
  •   Sims, Aidan
  •   Webster, Samuel B. (external author)

Publication Date


  • 2015

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84941417022

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5504&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4483

Has Global Citation Frequency


Number Of Pages


  • 21

Start Page


  • 657

End Page


  • 678

Volume


  • 363

Issue


  • 1

Place Of Publication


  • Germany

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 (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.

UOW Authors


  •   Laca, Marcelo (external author)
  •   Larsen, Nadia S. (external author)
  •   Neshveyev, Sergey (external author)
  •   Sims, Aidan
  •   Webster, Samuel B. (external author)

Publication Date


  • 2015

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84941417022

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5504&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4483

Has Global Citation Frequency


Number Of Pages


  • 21

Start Page


  • 657

End Page


  • 678

Volume


  • 363

Issue


  • 1

Place Of Publication


  • Germany