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

TL;DR

This paper explores a non-symmetric tensor product of states and representations of Cuntz-Krieger algebras, demonstrating closure of certain KMS states and deriving new formulas for type III factor representations.

Contribution

It introduces a novel non-symmetric tensor product framework and provides new tensor product formulas for type III factor representations of Cuntz-Krieger algebras.

Findings

Set of KMS states is closed under the tensor product

Derived formulas for tensor products of type III factor representations

Different from existing results on tensor products of type III factors

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}.