Jones index of a quantum dynamical semigroup

2007/04/16 by Anilesh Mohari, Mohari, Anilesh
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Jones index #Operator Algebras (math.OA) #Probability (math.PR) #Spectral Theory in Mathematical Physics #Sub-factor #completely positive maps

paper · pdf · doi:10.48550/arxiv.0704.1989

openalex publication_date 2007/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \cla₀ 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-II₁ factor.

Related

• Markov shift in Non-commutative Probability-II
• The index of a quantum dynamical semigroup
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• Pure inductive limit state and Kolmogorov's property-II
• Markov shift on non-commutative probability