Cocycle conjugacy of quasifree endomorphisms semigroups on the CAR algebra

Details Cocycle conjugacy of quasifree endomorphisms semigroups on the CAR algebra Cocycle conjugacy of quasifree endomorphisms semigroups on the CAR algebra

2000-10-18

arxiv.org/abs/math/0010183v2

Mathematics

Operator Algebras

15 pages, Latex

Scientific paper

W. Arveson has described a cocycle conjugacy class $U(\alpha)$ of $E_0$-semigroup $\alpha$ on B(H) which is a factor of type $\rm I$. Under some conditions on $\alpha$, there is a $E_0$-semigroup $\beta \in U(\alpha)$ being a flow of shifts in the sence of R.T. Powers. We study quasifree endomorphisms semigroups $\alpha$ on the hyperfinite factor $M=\pi (A(K))''$ generated by the representations $\pi$ of the algebra of canonical anticommutation relations A(K) over a separable Hilbert space K. The type of M can be $\rm I$, $\rm II$ or $\rm III$ depending on $\pi$. The cocycle conjugacy class $U(\alpha)$ is described in the terms of initial isometrical semigroups in K and an analogue of the Arveson result for the hyperfinite factors M of the type $\rm II_1$ and $\rm III_{\lambda}, 0<\lambda <1,$ is introduced.

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