Induced and amenable ergodic actions of Lie groups

Robert J. Zimmer

Annales scientifiques de l'École Normale Supérieure (1978)

  • Volume: 11, Issue: 3, page 407-428
  • ISSN: 0012-9593

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Zimmer, Robert J.. "Induced and amenable ergodic actions of Lie groups." Annales scientifiques de l'École Normale Supérieure 11.3 (1978): 407-428. <http://eudml.org/doc/82020>.

@article{Zimmer1978,
author = {Zimmer, Robert J.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Amenable Ergodic Action; Algebraic Group; Connected Semisimple Lie Group; Orbit of Any Probability Measure; Free Ergodic Action; Hyperfinite Von Neumann Algebra; Cocycle; Induced Ergodic Action},
language = {eng},
number = {3},
pages = {407-428},
publisher = {Elsevier},
title = {Induced and amenable ergodic actions of Lie groups},
url = {http://eudml.org/doc/82020},
volume = {11},
year = {1978},
}

TY - JOUR
AU - Zimmer, Robert J.
TI - Induced and amenable ergodic actions of Lie groups
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1978
PB - Elsevier
VL - 11
IS - 3
SP - 407
EP - 428
LA - eng
KW - Amenable Ergodic Action; Algebraic Group; Connected Semisimple Lie Group; Orbit of Any Probability Measure; Free Ergodic Action; Hyperfinite Von Neumann Algebra; Cocycle; Induced Ergodic Action
UR - http://eudml.org/doc/82020
ER -

References

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  1. [1] W. AMBROSE, Representation of Ergodic Flows (Annals of Math., Vol. 42, 1941, pp. 723-739). Zbl0025.26901MR3,52cJFM67.0421.01
  2. [2] A. BOREL, Linear Algebraic Groups, Benjamin, New York, 1969. Zbl0186.33201MR40 #4273
  3. [3] J. DIXMIER, Représentations induites holomorphes des groupes resoluble algébriques (Bull. Soc. Math. France) Vol. 94, 1966, pp. 181-206). Zbl0204.44101MR34 #7724
  4. [4] E. G. EFFROS, Transformation groups and C*-Algebras (Annals of Math., Vol. 81, 1965, pp. 38-55). Zbl0152.33203MR30 #5175
  5. [5] J. FELDMAN and C. C. MOORE, Ergodic Equivalence Relations, Cohomology, and von Neumann Algebras (Trans. Amer. Math. Soc., Vol. 234, 1977, pp. 289-360). Zbl0369.22009MR58 #28261a
  6. [6] J. FELDMAN, P. HAHN, and C. C. MOORE, Orbit Structure and Countable Sections for Actions of Continuous Groups. (Advances in Math., Vol. 28, 1978, pp. 186-230). Zbl0392.28023MR58 #11217
  7. [7] H. FURSTENBERG, A Poisson Formula for Semi-Simple Lie Groups (Annals of Math., Vol. 77, 1963, pp. 335-383). Zbl0192.12704MR26 #3820
  8. [8] H. FURSTENBERG, Boundary Theory and Stochastic Processes on Homogeneous Spaces, in Harmonic Analysis on Homogeneous Spaces (Symposia in Pure Mathematics, Williamstown, Mass., 1972). Zbl0289.22011
  9. [9] Y. GUIVARCH, Croissance polynomials et périodes des fonctions harmoniques (Bull. Soc. Math. France, Vol. 101, 1973, pp. 333-379). Zbl0294.43003MR51 #5841
  10. [10] G. W. MACKEY, Induced Representations of Locally Compact Groups, I (Annals of Math., Vol. 55, 1952, pp. 101-139). Zbl0046.11601MR13,434a
  11. [11] G. W. MACKEY, Point Realizations of Transformation Groups, (Illinois J. Math., Vol. 6, 1962, pp. 327-335). Zbl0178.17203MR26 #1424
  12. [12] G. W. MACKEY, Ergodic Theory and Virtual Groups (Math. Ann., Vol. 166, 1966, pp. 187-207). Zbl0178.38802MR34 #1444
  13. [13] G. W. MACKEY, Ergodic Theory and its Significance for Statistical Mechanics and Probability Theory (Advances in Math., Vol. 12, 1974, pp. 178-268). Zbl0326.60001MR49 #10857
  14. [14] C. C. MOORE, Ergodicity of Flows on Homogeneous Spaces (Amer. J. Math., Vol. 88, 1966, pp. 154-178). Zbl0148.37902MR33 #1409
  15. [15] A. RAMSAY, Virtual Groups and Group Actions (Advances in Math., Vol. 6, 1971, pp. 253-322). Zbl0216.14902MR43 #7590
  16. [16] C. SERIES, The Rohlin Theorem and Hyperfiniteness for Actions of Continuous Groups (to appear). Zbl0398.22013
  17. [17] V. S. VARADARAJAN, Geometry of Quantum Theory, Vol. II, van Nostrand, Princeton, N. J., 1970. Zbl0194.28802MR57 #11400
  18. [18] R. J. ZIMMER, Extensions of Ergodic Group Actions (Illinois J. Math., Vol. 20, 1976, pp. 373-409). Zbl0334.28015MR53 #13522
  19. [19] R. J. ZIMMER, Amenable Ergodic Actions, Hyperfinite Factors, and Poincaré Flows (Bull. Amer. Math. Soc., Vol. 83, 1977, pp. 1078-1080). Zbl0378.28008MR57 #591
  20. [20] R. J. ZIMMER, Amenable Ergodic Group Actions and an Application to Poisson Boundaries of Random Walks (J. Funct. Anal., Vol. 27, 1978, pp. 350-372). Zbl0391.28011MR57 #12775
  21. [21] R. J. ZIMMER, On the von Neumann Algebra of an Ergodic Group Action (Proc. Amer. Math. Soc., Vol. 66, 1977, pp. 289-293). Zbl0367.28013MR57 #592
  22. [22] R. J. ZIMMER, Hyperfinite Factors and Amenable Ergodic Actions (Invent. Math., Vol. 41, 1977, pp. 23-31). Zbl0361.46061MR57 #10438
  23. [23] R. J. ZIMMER, Amenable Pairs of Groups and Ergodic Actions and the Associated von Neumann Algebras [Trans. Amer. Math. Soc. (to appear)]. Zbl0408.22011
  24. [24] R. J. ZIMMER, Orbit Spaces of Unitary Representations, Ergodic Theory, and Simple Lie Groups (Ann. of Math., Vol. 106, 1977, pp. 573-588). Zbl0393.22006MR57 #6286
  25. [25] P. HAHN, The σ-Representations of Amenable Groupoids, preprint. 

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