English

Generalized CCR Flows

Operator Algebras 2009-11-13 v1 Functional Analysis

Abstract

We introduce a new construction of E0E_0-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of C0C_0-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 E0E_0-semigroups, which can not be distinguished from E0E_0-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 E0E_0-semigroup, we show that there exist uncountably many type III E0E_0-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}
}
R2 v1 2026-06-21T08:30:53.943Z