Boyko M. Dynamical entropy for automorphisms of groups and group algebras

Dynamical entropy for automorphisms of group and automorphisms of W*-(C*-) algebras. Calculation and estimation of entropy for classes of automorphisms of groups and С*-algebras. Methods of entropy theory, asymptotic theory for characters of the big groups, theory of symmetric and supersymmetric functions, methods of harmonic analysis. Explicit formula for calculation of the CNT-entropy for the shift automorphism on II_1-factor-representations of symmetric group is obtained, we obtain explicit formula for the CNT-entropy for the Bogoliubov automorphisms on II_1-factor-representations of unitary group except those ones which correspond to a unitary operator with singular and representation with gamma^+ + gamma^- > 0, methods for the calculation of the Choda entropy for automorphisms of discrete groups are developed, estimation for the Voiculescu entropy for a class of automorphisms of С*-algebras is obtained. The results are important for investigations of ergodic properties of automorphisms of operatoralgebras and for further study of entropy for automorphisms of discrete groups.