Jones index of a quantum dynamical semigroup

Details Jones index of a quantum dynamical semigroup Jones index of a quantum dynamical semigroup

2007-04-16

arxiv.org/abs/0704.1989v1

Mathematics

Operator Algebras

Scientific paper

In this paper we consider a semigroup of completely positive maps $\tau=(\tau_t,t \ge 0)$ with a faithful normal invariant state $\phi$ on a type-$II_1$ factor $\cla_0$ and propose an index theory. We :achieve this via a more general Kolmogorov's type of construction for stationary Markov processes which naturally associate a nested isomorphic von-Neumann algebras. In particular this construction generalizes well known Jones construction associated with a sub-factor of type-II$_1$ factor.

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