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.
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