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

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${}_{\lambda }$ factors, for $\lambda \in (0,1]$.

40 pages

Cited by in corpus (1)

• On the classification and modular extendability of E${}_0$-semigroups on factors