On Cocycle Conjugacy of Quasifree Endomorphisms Semigroups on the Car Algebra

W. Arveson has described a cocycle conjugacy class U(α) of E0-semigroup α on B(H) which is a factor of type I. Under some conditions on α there is a E0-semigroup β ∈ U(α) being a flow of shifts in the sense of R.T.Powers (see [11]). We study quasifree endomorphisms semigroups α on the hyperfinite factor M = π(A(K)) generated by the representation π of the algebra of the canonical anticommutation relations A(K) over a separable Hilbert space K. The type of M can be I, II or III depending on π. The cocycle conjugacy class U(α) is described in the terms of initial isometrical semigroup in K and an analogue of the Arveson result for the hyperfinite factor M of type II1 and IIIλ, 0 < λ < 1, is introduced.