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arXiv · 1404.5934

Non-cocycle-conjugate $E_0$-semigroups on factors

Oliver T. Margetts·R. Srinivasan
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Abstract

We investigate $E_0-$semigroups on general factors, which are not necessarily of type I, and analyse associated invariants like product systems, super product systems etc. By tensoring $E_0-$semigroups on type I factors with $E_0-$semigroups on type II$_1$ factor, we produce several families (both countable and uncountable), consisting of mutually non-cocycle-conjugate of $E_0-$semigroups on the hyperfinite II$_\infty$ factor. Using CCR representations associated with quasi-free states, we construct for the first time, uncountable families consisting of mutually non-cocycle-conjugate $E_0-$semigroups on all type III$_λ$ factors, for $λ\in (0,1]$.

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BibTeXRIS

Oliver T. Margetts, R. Srinivasan. 2014-09-25. Non-cocycle-conjugate $E_0$-semigroups on factors. https://arxiv.org/abs/1404.5934

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