Non-Cocycle-Conjugate E$_0$-Semigroups on Factors
Oliver T. Margetts, R. Srinivasan · Publications of the Research Institute for Mathematical Sciences · 2017
We investigate E _0 -semigroups on general factors, which are not necessarily of type I or II _1 . We show several families on the hyperfinite II _\infty factor, which arises as tensor products, consists of mutually non-cocycle-conjugate E _0 -semigroups. Using CCR representations associated with quasi-free states, we exhibit, 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] . They are not cocycle conjugate to the E _0 -semigroups constructed using CAR representations.