ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46, 47 ,81, 82 Golodets Valentin, Institute for Low Temperature Physics, Kharkov, Ukraine Dynamical entropy and quantum K-systems The notion of dynamical entropy for automorphisms of C^{∗}-algebras was introduced by Connes, Narnhofer and Thirring. In recent years, some progress in the computation of CNT-entropy in different models was made. Narnhofer and Thirring suggested a quantum version of Kolmogorov systems (K-systems). Such systems are important in commutative theory. We prove that a wide class of quantum models possess the K-property. In particular, a quantum lattice with finite range of intersection and the ideal of Bose and Fermi (even part) gases belong to this class. An uncountable family of pairwise non-conjugate non-Bernoullian K-systems of type III_{1} with the same entropy is constructed. S. Neshveyev took part in this research.