多参数CAR流的可分解性

摘要：

设$P$是$\mathbb{R}^d$中的一个闭凸锥，它被假定为是跨越$\mathbb{R}^d$的，并且不包含直线。在这篇文章中，我们考虑了一族在$P$上的CAR流，并研究了相关乘积系统的可分解性。建立了CAR流可分解的充要条件。因此，我们表明，有无数的CAR流的上循环共轭相应的CCR流。

英文摘要：

Let $P$ be a closed convex cone in $\mathbb{R}^d$ which is assumed to be spanning $\mathbb{R}^d$ and contains no line. In this article, we consider a family of CAR flows over $P$ and study the decomposability of the associated product systems. We establish a necessary and sufficient condition for CAR flow to be decomposable. As a consequence we show that there are uncountable many CAR flows which are cocycle conjugate to the corresponding CCR flows.

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