ArticleOriginal scientific text
Title
On group extensions of 2-fold simple ergodic actions
Authors 1
Affiliations
- Department of Mathematics, Agricultural and Technical Academy of Olsztyn, Oczapowskiego 1, 10-740 Olsztyn-Kortowo, Poland.
Abstract
Compact group extensions of 2-fold simple actions of locally compact second countable amenable groups are considered. It is shown what the elements of the centralizer of such a system look like. It is also proved that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.
Bibliography
- F. P. Greenleaf, Ergodic theorems and the construction of summing sequences in amenable locally compact groups, Comm. Pure Appl. Math. 26 (1973), 29-46.
- A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557.
- U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985.
- M. Lemańczyk, Ergodic compact abelian group extensions of rotations, preprint, Toruń, 1990.
- M. Lemańczyk and M. K. Mentzen, Compact subgroups in the centralizer of natural factors of an ergodic group extension of a rotation determine all factors, Ergodic Theory Dynamical Systems 10 (1990), 763-776.
- G. W. Mackey, Ergodic transformation groups with a pure point spectrum, Illinois J. Math. 8 (1964), 593-600.
- M. K. Mentzen, Ergodic properties of group extensions of dynamical systems with discrete spectra, Studia Math. 101 (1991), 19-31.
- D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136.
- W. A. Veech, A criterion for a process to be prime, Monatsh. Math. 94 (1982), 335-341.