Communications in Mathematical Physics

, Volume 281, Issue 2, pp 529–571

Generalized CCR Flows

Article

DOI: 10.1007/s00220-008-0447-z

Cite this article as:
Izumi, M. & Srinivasan, R. Commun. Math. Phys. (2008) 281: 529. doi:10.1007/s00220-008-0447-z

Abstract

We introduce a new construction of E0-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of C0-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 E0-semigroups, which can not be distinguished from E0-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 E0-semigroup, we show that there exist uncountably many type III E0-semigroups in this family, which are mutually non-cocycle conjugate.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan
  2. 2.Chennai Mathematical InstituteSiruseriIndia

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