Tensor products of type III factor representations of Cuntz-Krieger algebras

2008/05/06 by Kawamura, Katsunori
#46K10 #46L30 #46L35 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.0805.0667

Abstract

We introduced a non-symmetric tensor product of any two states or any two representations of Cuntz-Krieger algebras associated with a certain non-cocommutative comultiplication in previous our work. In this paper, we show that a certain set of KMS states is closed with respect to the tensor product. From this, we obtain formulae of tensor product of type \rm III factor representations of Cuntz-Krieger algebras which is different from results of the tensor product of factors of type \rm III.

Related

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• A tensor product for representations of the Cuntz algebra and of the R. Thompson groups
• A tensor product of representations of UHF algebras arising from Kronecker products
• The Cuntz semigroup of the tensor product C*-algebras
• C^*-bialgebra defined by the direct sum of Cuntz-Krieger algebras