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CAR flows on type III factors and their extendability

Panchugopal Bikram

Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva-84105, Israel

https://doi.org/10.1142/S021902571450026XCited by:4 (Source: Crossref)

Abstract

In this paper we prove that the CAR flows on type III factors arising from a large class of quasi-free states are not extendable, in the sense of Bikram, Izumi, Srinivasan and Sunder.⁸ As a consequence, CAR flows and CCR flows on type III factors are not cocycle conjugate. This is in sharp contrast with the situation for the type I_∞ factor, for which CAR and CCR flows are in fact conjugate. In addition, we also compute the super-product systems associated to CAR flows.

Keywords:

AMSC: Primary 46L55, Secondary 46L40, Secondary 46L53, Secondary 46C99

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