Decomposability of multiparameter CAR flows

Abstract

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.