Non-cocycle-conjugate E₀-semigroups on factors

2014/04/23 by Oliver T. Margetts, R. Srinivasan, Margetts, Oliver T. +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1404.5934

openalex publication_date 2014/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate E₀-semigroups on general factors, which are not necessarily of type I, and analyse associated invariants like product systems, super product systems etc. By tensoring E₀-semigroups on type I factors with E₀-semigroups on type II₁ factor, we produce several families (both countable and uncountable), consisting of mutually non-cocycle-conjugate of E₀-semigroups on the hyperfinite II_∞ factor. Using CCR representations associated with quasi-free states, we construct for the first time, uncountable families consisting of mutually non-cocycle-conjugate E₀-semigroups on all type III_λ factors, for λ∈ (0,1].

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