算子代数上的连续流和离散流
Continuous and discrete flows on operator algebras
摘要：
设$(N,\R,θ)$是一个中心遍历W* 动力系统.当$N$不是因子时，我们证明了对于每个$t\not=0$，由时间$t$自同构$θ_t$诱导的交叉积不是因子当且仅当存在有理数$r$和$θ$对$N$中心的限制的特征值$s$，使得$rst=2π$ .在C* 设定中，极小性似乎是对应于中心遍历性的概念。证明了如果$(A,\R,α)$是极小有单位C* 动力系统，且$A$是素数或交换但不简单，则对每个$t\not=0$，由时间$t$自同构$α_t$诱导的交叉积不简单当且仅当存在有理数$r$和$α$限制到$A$中心的特征值$s$，使得$rst=2π$ .
英文摘要：
Let $(N,\R,θ)$ be a centrally ergodic W* dynamical system. When $N$ is not a factor, we show that, for each $t\not=0$, the crossed product induced by the time $t$ automorphism $θ_t$ is not a factor if and only if there exist a rational number $r$ and an eigenvalue $s$ of the restriction of $θ$ to the center of $N$, such that $rst=2π$. In the C* setting, minimality seems to be the notion corresponding to central ergodicity. We show that if $(A,\R,α)$ is a minimal unital C* dynamical system and $A$ is either prime or commutative but not simple, then, for each $t\not=0$, the crossed product induced by the time $t$ automorphism $α_t$ is not simple if and only if there exist a rational number $r$ and an eigenvalue $s$ of the restriction of $α$ to the center of $A$, such that $rst=2π$.
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