On the entropy for actions of some class of groups and its calculation

Communicated by V.Ya. Golodets

Анотація

The dynamical entropy for actions of ÅZ_k; k = 2 ; 3 ; : : :; on C - algebras which is studied in this work, is a generalization of Connes-Narnhofer-Thirring entropy for actions of the torsion groups on C-algebras. The properties of such entropy are investigated and a formula for quantum dy- namical entropy of the Bogoliubov action of ÅZ_k; k = 2 ; 3 ; : : :;on the CAR- algebra is obtained. It is proved that the part of action corresponding to the singular spectrum gives zero contribution to the entropy.