# Semisimplicity, joinings and group extensions

A. Del Junco; M. Lemańczyk; M. Mentzen

Studia Mathematica (1995)

- Volume: 112, Issue: 2, page 141-164
- ISSN: 0039-3223

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topDel Junco, A., Lemańczyk, M., and Mentzen, M.. "Semisimplicity, joinings and group extensions." Studia Mathematica 112.2 (1995): 141-164. <http://eudml.org/doc/216143>.

@article{DelJunco1995,

abstract = {We present a theory of self-joinings for semisimple maps and their group extensions which is a unification of the following three cases studied so far: (iii) Gaussian-Kronecker automorphisms: [Th], [Ju-Th]. (ii) MSJ and simple automorphisms: [Ru], [Ve], [Ju-Ru]. (iii) Group extension of discrete spectrum automorphisms: [Le-Me], [Le], [Me].},

author = {Del Junco, A., Lemańczyk, M., Mentzen, M.},

journal = {Studia Mathematica},

keywords = {semisimple maps; ergodic automorphism; minimal self-joinings; ergodic group extensions},

language = {eng},

number = {2},

pages = {141-164},

title = {Semisimplicity, joinings and group extensions},

url = {http://eudml.org/doc/216143},

volume = {112},

year = {1995},

}

TY - JOUR

AU - Del Junco, A.

AU - Lemańczyk, M.

AU - Mentzen, M.

TI - Semisimplicity, joinings and group extensions

JO - Studia Mathematica

PY - 1995

VL - 112

IS - 2

SP - 141

EP - 164

AB - We present a theory of self-joinings for semisimple maps and their group extensions which is a unification of the following three cases studied so far: (iii) Gaussian-Kronecker automorphisms: [Th], [Ju-Th]. (ii) MSJ and simple automorphisms: [Ru], [Ve], [Ju-Ru]. (iii) Group extension of discrete spectrum automorphisms: [Le-Me], [Le], [Me].

LA - eng

KW - semisimple maps; ergodic automorphism; minimal self-joinings; ergodic group extensions

UR - http://eudml.org/doc/216143

ER -

## References

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- [Ju-Ru] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557. Zbl0646.60010
- [Ju-Th] A. del Junco and J.-P. Thouvenot, The theory for Gaussian-Kronecker automorphisms, preprint.
- [Ke-Ne1] H. B. Keynes and D. Newton, Choquet Theory and Ergodic Measures for Compact Group Extensions, Lecture Notes in Math. 318, Springer, 1973. Zbl0256.28014
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- [Le] M. Lemańczyk, Ergodic abelian group extensions of rotations, preprint, Toruń 1990.
- [Le] 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
- [Me] M. K. Mentzen, Ergodic properties of group extensions of dynamical systems with discrete spectra, Studia Math. 101 (1991), 19-31. Zbl0809.28015
- [Ne] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136. Zbl0425.28012
- [Ne1] D. Newton, Coalescence and spectrum of automorphisms of a Lebesgue space, Z. Wahrsch. Verw. Gebiete 19 (1971), 117-122. Zbl0201.38401
- [Ru] D. Rudolph, An example of measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122. Zbl0446.28018
- [Ru1] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, ibid. 34 (1978), 36-60. Zbl0415.28012
- [Th] J.-P. Thouvenot, The metrical structure of some Gaussian processes, in: Proc. Ergodic Theory and Related Topics II, Georgenthal 1986, 195-198.
- [Ve] W. A. Veech, A criterion for a process to be prime, Monatsh. Math. 94 (1982), 335-341. Zbl0499.28016
- [Zi] R. Zimmer, Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373-409. Zbl0334.28015
- [Zi1] R. Zimmer, Ergodic actions with generalized discrete spectrum, ibid., 555-588. Zbl0349.28011

## Citations in EuDML Documents

top- Andrés del Junco, Mariusz Lemańczyk, Simple systems are disjoint from Gaussian systems
- T. Downarowicz, Jan Kwiatkowski, Y. Lacroix, Spectral isomorphisms of Morse flows
- Mariusz Lemańczyk, F. Parreau, J. Thouvenot, Gaussian automorphisms whose ergodic self-joinings are Gaussian
- M. Lemańczyk, Cohomology groups, multipliers and factors in ergodic theory
- Alexandre Danilenko, Mariusz Lemańczyk, Isometric extensions, 2-cocycles and ergodicity of skew products

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