Classification and realizations of type III factor representations of Cuntz-Krieger algebras associated with quasi-free states

Abstract

We completely classify type III factor representations of Cuntz-Krieger algebras associated with quasi-free states up to unitary equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free groups and their type ${\mathrm{II}}_1$ factor representations are used in these realizations.

11 pages

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