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On group extensions of 2-fold simple ergodic actions. (English) Zbl 0823.28006

Following the methods of M. Lemańczyk and M. K. Mentzen for \(\mathbb{Z}\)-actions [Ergodic Theory Dyn. Syst. 10, No. 4, 763-776 (1990; Zbl 0725.54030)], the author gives a description of the centralizer and the structure of factors for ergodic group extensions of 2-fold simple actions of a locally compact second countable amenable group on a standard Borel space. Just as in the \(\mathbb{Z}\)-action case, it is shown that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.

MSC:

28D05 Measure-preserving transformations
28D15 General groups of measure-preserving transformations

Citations:

Zbl 0725.54030
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