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.

非环共轭E $_{0}$ -因子半群

奥利弗·马盖茨

R.斯里尼瓦桑

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