Tensor Products of Type III Factor Representations of Cuntz-Krieger Algebras

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 our previous 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 products of type III factor representations of Cuntz-Krieger algebras which are different from results of the tensor product of factors of type III.