CAR flows on type III factors and its extendability

TL;DR

This paper proves that CAR flows on type III factors from most quasi-free states are not extendable, revealing differences from CCR flows and providing insights into their super product systems and cocycle conjugacy properties.

Contribution

It establishes non-extendability of CAR flows on type III factors and distinguishes their cocycle conjugacy class from CCR flows, advancing understanding of flow structures.

Findings

CAR flows on type III factors are not extendable

CAR flows and CCR flows on type III factors are not cocycle conjugate

Super product system of CAR flows is characterized

Abstract

In this paper using one of the necessary conditions obtained for extendability in [BISSar], we prove that the CAR flows ([Amo01]) on type III factors arising from most quasi-free states are not extendable. As a consequence we find the super product system of CAR flows. We know from [Arv03] that CCR flows and CAR flows on type I factors with the same Arveson index are cocycle conjugate. But our result together with [BISSar] will show that CCR flows and CAR flows on type III factors are not cocycle conjugate.