Generalized CCR Flows
Operator Algebras
2009-11-13 v1 Functional Analysis
Abstract
We introduce a new construction of -semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of -semigroups. We get a new necessary and sufficient condition for them to be of type III, when the associated sum system is of finite index. Using this criterion, we construct examples of type III -semigroups, which can not be distinguished from -semigroups of type I by the invariants introduced by Boris Tsirelson. Finally, by considering the local von Neumann algebras, and by associating a type III factor to a given type III -semigroup, we show that there exist uncountably many type III -semigroups in this family, which are mutually non-cocycle conjugate.
Keywords
Cite
@article{arxiv.0705.3280,
title = {Generalized CCR Flows},
author = {Masaki Izumi and R. Srinivasan},
journal= {arXiv preprint arXiv:0705.3280},
year = {2009}
}