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- Title
Jones Index of a Quantum Dynamical Semigroup.
- Authors
Mohari, Anilesh
- Abstract
In this paper we consider a semigroup of completely positive maps τ=( τ t, t≥0) with a faithful normal invariant state φ on a type- II1 factor $\mathcal{A}_{0}$ and propose an index theory. We achieve this via a Kolmogorov’s type of construction for stationary Markov processes which naturally associate a nested family of isomorphic von-Neumann algebras. In particular this construction generalises well known Jones construction associated with a sub-factor of a type-II1 factor.
- Subjects
INDEX theory (Mathematics); MARKOV processes; MATHEMATICAL analysis; VON Neumann algebras; HILBERT space; ENDOMORPHISMS; GROUP theory
- Publication
Acta Applicandae Mathematicae, 2009, Vol 108, Issue 3, p665
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-008-9426-9