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Type III von Neumann algebras associated with 2‐graphs

Type III von Neumann algebras associated with 2‐graphs Let 픽θ+ be a 2‐graph, where θ is a permutation encoding the factorization property in the 2‐graph, and ω be a distinguished faithful state associated with its graph C*‐algebra. In this paper, we characterize the factorness of the von Neumann algebra induced from the Gelfand‐Naimark‐Segal representation of ω under a certain condition. Moreover, its type is further determined when it is a factor. In the case of θ being the identity permutation, our condition turns out to be redundant. On the way to our main results, we also obtain the structure of the fixed point algebra of the modular action given by ω. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Type III von Neumann algebras associated with 2‐graphs

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References (32)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdr132
Publisher site
See Article on Publisher Site

Abstract

Let 픽θ+ be a 2‐graph, where θ is a permutation encoding the factorization property in the 2‐graph, and ω be a distinguished faithful state associated with its graph C*‐algebra. In this paper, we characterize the factorness of the von Neumann algebra induced from the Gelfand‐Naimark‐Segal representation of ω under a certain condition. Moreover, its type is further determined when it is a factor. In the case of θ being the identity permutation, our condition turns out to be redundant. On the way to our main results, we also obtain the structure of the fixed point algebra of the modular action given by ω.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Aug 1, 2012

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