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Dynamical entropy for Bogoliubov actions of torsion-free abelian groups on the CAR-algebra

Published online by Cambridge University Press:  01 August 2000

VALENTIN YA. GOLODETS
Affiliation:
Institute for Low Temperature Physics and Engineering, Lenin Ave 47, Kharkov 310164, Ukraine (e-mail: {golodets,neshveyev}@ilt.kharkov.ua)
SERGEY V. NESHVEYEV
Affiliation:
Institute for Low Temperature Physics and Engineering, Lenin Ave 47, Kharkov 310164, Ukraine (e-mail: {golodets,neshveyev}@ilt.kharkov.ua)

Abstract

We compute dynamical entropy in Connes, Narnhofer and Thirring sense for a Bogoliubov action of a torsion-free abelian group $G$ on the CAR-algebra. A formula analogous to that found by Størmer and Voiculescu in the case $G={\Bbb Z}$ is obtained. The singular part of a unitary representation of $G$ is shown to give zero contribution to the entropy. A proof of these results requires new arguments since a torsion-free group may have no finite index proper subgroups. Our approach allows us to overcome these difficulties, it differs from that of Størmer–Voiculescu.

Type
Research Article
Copyright
2000 Cambridge University Press

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