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

Published online by Cambridge University Press:  02 April 2001

SERGEY I. BEZUGLYI
Affiliation:
Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Vienna, Austria
VALENTIN YA. GOLODETS
Affiliation:
Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Vienna, Austria

Abstract

The notion of dynamical entropy for actions of a countable free abelian group $G$ by automorphisms of $C^*$-algebras is studied. These results are applied to Bogoliubov actions of $G$ on the CAR-algebra. It is shown that the dynamical entropy of Bogoliubov actions is computed by a formula analogous to that found by Størmer and Voiculescu in the case $G={\bf Z}$, and also it is proved that the part of the action corresponding to a singular spectrum gives zero contribution to the entropy. The case of an infinite number of generators has some essential differences and requires new arguments.

Type
Research Article
Copyright
© 1997 Cambridge University Press

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