On group extensions of 2-fold simple ergodic actions

Artur Siemaszko

Studia Mathematica (1994)

  • Volume: 110, Issue: 1, page 53-64
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Siemaszko, Artur. "On group extensions of 2-fold simple ergodic actions." Studia Mathematica 110.1 (1994): 53-64. <http://eudml.org/doc/216098>.

@article{Siemaszko1994,
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.},
author = {Siemaszko, Artur},
journal = {Studia Mathematica},
keywords = {centralizer; ergodic group extensions; simple actions; normal factor},
language = {eng},
number = {1},
pages = {53-64},
title = {On group extensions of 2-fold simple ergodic actions},
url = {http://eudml.org/doc/216098},
volume = {110},
year = {1994},
}

TY - JOUR
AU - Siemaszko, Artur
TI - On group extensions of 2-fold simple ergodic actions
JO - Studia Mathematica
PY - 1994
VL - 110
IS - 1
SP - 53
EP - 64
AB - 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.
LA - eng
KW - centralizer; ergodic group extensions; simple actions; normal factor
UR - http://eudml.org/doc/216098
ER -

References

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  1. [1] F. P. Greenleaf, Ergodic theorems and the construction of summing sequences in amenable locally compact groups, Comm. Pure Appl. Math. 26 (1973), 29-46. Zbl0243.22005
  2. [2] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557. Zbl0646.60010
  3. [3] U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985. 
  4. [4] M. Lemańczyk, Ergodic compact abelian group extensions of rotations, preprint, Toruń, 1990. 
  5. [5] 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. Zbl0725.54030
  6. [6] G. W. Mackey, Ergodic transformation groups with a pure point spectrum, Illinois J. Math. 8 (1964), 593-600. Zbl0255.22014
  7. [7] M. K. Mentzen, Ergodic properties of group extensions of dynamical systems with discrete spectra, Studia Math. 101 (1991), 19-31. Zbl0809.28015
  8. [8] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136. Zbl0425.28012
  9. [9] W. A. Veech, A criterion for a process to be prime, Monatsh. Math. 94 (1982), 335-341. Zbl0499.28016

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