# Jones index of a quantum dynamical semigroup - Mathematics Operator Algebras

Abstract: 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 atype-$II 1$ factor $\cla 0$ and propose an index theory. We :achieve this via amore general Kolmogorovs type of construction for stationary Markov processeswhich naturally associate a nested isomorphic von-Neumann algebras. Inparticular this construction generalizes well known Jones constructionassociated with a sub-factor of type-II$1$ factor.

Author: Anilesh Mohari

Source: https://arxiv.org/