COCYCLE PERTURBATION OF QUASIFREE ALGEBRAIC K-FLOW LEADS TO REQUIRED ASYMPTOTIC DYNAMICS OF ASSOCIATED COMPLETELY POSITIVE SEMIGROUP

Abstract

We study the quasifree algebraic K-flow τ on the hyperfinite factor ℳ with the expanding subfactor [Formula: see text] generated by representations π of the C*-algebra of the canonical anticommutation relations (CAR) [Formula: see text] over separable Hilbert space ℋ. The type of ℳ and [Formula: see text] can be II1 or IIIλ, 0<λ<1, depending on π. The K-flow τ is obtained by the quasifree lifting of one-parameter group ST consisting of shifts in ℋ with the discrete parameter T=Z or the continuous one T=R. We prove that acting on τ by a quasifree inner Markovian cocycle, one can get the required asymptotic behavior of the perturbed group restriction on [Formula: see text].