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1999 | 137 | 2 | 123-142
Tytuł artykułu

Isometric extensions, 2-cocycles and ergodicity of skew products

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension $T_α$ and admits a prescribed subgroup in the centralizer of $T_α$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
137
Numer
2
Strony
123-142
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-09-22
poprawiono
1999-08-30
Twórcy
  • Department of Mechanics and Mathematics, Kharkov State University, Freedom sq. 4 Kharkov, 310077, Ukraine , danilenko@ilt.kharkov.ua
  • Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland , mlem@mat.uni.torun.pl
Bibliografia
  • [Br] L. G. Brown, Topologically complete groups, Proc. Amer. Math. Soc. 35 (1972), 593-600.
  • [D1] A. I. Danilenko, Comparison of cocycles of measured equivalence relations and lifting problems, Ergodic Theory Dynam. Systems 18 (1998), 125-151.
  • [D2] A. I. Danilenko, On cocycles with values in group extensions. Generic results, Mat. Analiz Geom., to appear.
  • [DG] A. I. Danilenko and V. Ya. Golodets, Extension of cocycles to normalizer elements, outer conjugacy and related problems, Trans. Amer. Math. Soc. 348 (1996), 4857-4882.
  • [FL] S. Ferenczi and M. Lemańczyk, Rank is not a spectral invariant, Studia Math. 98 (1991), 227-230.
  • [GLS] P. Gabriel, M. Lemańczyk and K. Schmidt, Extensions of cocycles for hyperfinite actions and applications, Monatsh. Math. 123 (1997), 209-228.
  • [Ha] T. Hamachi, On a minimal group cover of an ergodic finite extension, preprint.
  • [JLM] A. del Junco, M. Lemańczyk and M. Mentzen, Semisimplicity, joinings, and group extensions, Studia Math. 112 (1995), 141-164.
  • [Ki] J. King, The commutant is the weak closure of the powers, for rank-1 transformations, Ergodic Theory Dynam. Systems 6 (1986), 363-384.
  • [Kw] J. Kwiatkowski, Factors of ergodic group extensions of rotations, Studia Math. 103 (1992), 123-131.
  • [Le] M. Lemańczyk, Cohomology groups, multipliers and factors in ergodic theory, ibid. 122 (1997), 275-288.
  • [Me] M. K. Mentzen, Ergodic properties of group extensions of dynamical systems with discrete spectra, ibid. 101 (1991), 20-31.
  • [Ne] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136.
  • [Pa] K. R. Parthasarathy, Multipliers on Locally Compact Groups, Lecture Notes in Math. 93, Springer, 1969.
  • [Sc] K. Schmidt, Lectures on Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, Macmillan, 1977.
  • [Z1] R. Zimmer, Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373-409.
  • [Z2] R. Zimmer, Ergodic Theory and Semisimple Lie Groups, Birkhäuser, Boston, 1984.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv137i2p123bwm
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