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arXiv · 0705.3280

Generalized CCR Flows

Masaki Izumi·R. Srinivasan
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Abstract

We introduce a new construction of $E_0$-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of $C_0$-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 $E_0$-semigroups, which can not be distinguished from $E_0$-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 $E_0$-semigroup, we show that there exist uncountably many type III $E_0$-semigroups in this family, which are mutually non-cocycle conjugate.

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Masaki Izumi, R. Srinivasan. 2007-05-23. Generalized CCR Flows. https://doi.org/10.1007/s00220-008-0447-z

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