Complete positivity of entropy and non-Bernoullicity for transformation groups

Valentin Golodets; Sergey Sinel'shchikov

Colloquium Mathematicae (2000)

  • Volume: 84/85, Issue: 2, page 421-429
  • ISSN: 0010-1354

Abstract

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The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.

How to cite

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Golodets, Valentin, and Sinel'shchikov, Sergey. "Complete positivity of entropy and non-Bernoullicity for transformation groups." Colloquium Mathematicae 84/85.2 (2000): 421-429. <http://eudml.org/doc/210823>.

@article{Golodets2000,
abstract = {The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.},
author = {Golodets, Valentin, Sinel'shchikov, Sergey},
journal = {Colloquium Mathematicae},
keywords = {complete positive entropy; Abelian group action},
language = {eng},
number = {2},
pages = {421-429},
title = {Complete positivity of entropy and non-Bernoullicity for transformation groups},
url = {http://eudml.org/doc/210823},
volume = {84/85},
year = {2000},
}

TY - JOUR
AU - Golodets, Valentin
AU - Sinel'shchikov, Sergey
TI - Complete positivity of entropy and non-Bernoullicity for transformation groups
JO - Colloquium Mathematicae
PY - 2000
VL - 84/85
IS - 2
SP - 421
EP - 429
AB - The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.
LA - eng
KW - complete positive entropy; Abelian group action
UR - http://eudml.org/doc/210823
ER -

References

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  1. [1] C J. P. Conze, Entropie d'un groupe abélien de transformations, Z. Wahrsch. Verw. Gebiete 25 (1972), 11-30. Zbl0261.28015
  2. [2] E. Glasner, J.-P. Thouvenot and B. Weiss, Entropy theory without past, preprint ESI-612. Zbl0965.37009
  3. [3] V. Golodets and S. Sinel'shchikov, On the entropy theory of finitely generated nilpotent group actions, preprint. 
  4. [4] B. Kamiński, The theory of invariant partitions for ℤ d -actions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 349-362. Zbl0479.28016
  5. [5] D. Ornstein and P. C. Shields, An uncountable family of K-automorphisms, Adv. Math. 10 (1973), 63-88. Zbl0251.28004
  6. [6] D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math. 48 (1987), 1-141. Zbl0637.28015
  7. [7] V. A. Rokhlin and Ya. G. Sinai, Construction and properties of invariant meas- urable partitions, Dokl. Akad. Nauk SSSR 141 (1961), 1038-1041 (in Russian). 
  8. [8] D. J. Rudolph and B. Weiss, Entropy and mixing for amenable group actions, preprint. Zbl0957.37003

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