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We completely classify type III factor representations of Cuntz-Kriegeralgebras associated with quasi-free states up to unitary equivalence.Furthermore, we realize these representations on concrete Hilbert spaceswithout using GNS construction. Free groups and their type ${\rm II}_{1}$factor representations are used in these realizations.

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