Induced and amenable ergodic actions of Lie groups
Zimmer, Robert J.
Annales scientifiques de l'École Normale Supérieure, Tome 11 (1978), p. 407-428 / Harvested from Numdam
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@article{ASENS_1978_4_11_3_407_0,
     author = {Zimmer, Robert J.},
     title = {Induced and amenable ergodic actions of Lie groups},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {11},
     year = {1978},
     pages = {407-428},
     doi = {10.24033/asens.1351},
     mrnumber = {81b:22013},
     zbl = {0401.22009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1978_4_11_3_407_0}
}

Zimmer, Robert J. Induced and amenable ergodic actions of Lie groups. Annales scientifiques de l'École Normale Supérieure, Tome 11 (1978) pp. 407-428. doi : 10.24033/asens.1351. http://gdmltest.u-ga.fr/item/ASENS_1978_4_11_3_407_0/

[1] W. Ambrose, Representation of Ergodic Flows (Annals of Math., Vol. 42, 1941, pp. 723-739). | JFM 67.0421.01 | MR 3,52c | Zbl 0025.26901

[2] A. Borel, Linear Algebraic Groups, Benjamin, New York, 1969. | MR 40 #4273 | Zbl 0186.33201

[3] J. Dixmier, Représentations induites holomorphes des groupes resoluble algébriques (Bull. Soc. Math. France) Vol. 94, 1966, pp. 181-206). | Numdam | MR 34 #7724 | Zbl 0204.44101

[4] E. G. Effros, Transformation groups and C*-Algebras (Annals of Math., Vol. 81, 1965, pp. 38-55). | MR 30 #5175 | Zbl 0152.33203

[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). | MR 58 #28261a | Zbl 0369.22009

[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). | MR 58 #11217 | Zbl 0392.28023

[7] H. Furstenberg, A Poisson Formula for Semi-Simple Lie Groups (Annals of Math., Vol. 77, 1963, pp. 335-383). | MR 26 #3820 | Zbl 0192.12704

[8] H. Furstenberg, Boundary Theory and Stochastic Processes on Homogeneous Spaces, in Harmonic Analysis on Homogeneous Spaces (Symposia in Pure Mathematics, Williamstown, Mass., 1972). | Zbl 0289.22011

[9] Y. Guivarch, Croissance polynomials et périodes des fonctions harmoniques (Bull. Soc. Math. France, Vol. 101, 1973, pp. 333-379). | Numdam | MR 51 #5841 | Zbl 0294.43003

[10] G. W. Mackey, Induced Representations of Locally Compact Groups, I (Annals of Math., Vol. 55, 1952, pp. 101-139). | MR 13,434a | Zbl 0046.11601

[11] G. W. Mackey, Point Realizations of Transformation Groups, (Illinois J. Math., Vol. 6, 1962, pp. 327-335). | MR 26 #1424 | Zbl 0178.17203

[12] G. W. Mackey, Ergodic Theory and Virtual Groups (Math. Ann., Vol. 166, 1966, pp. 187-207). | MR 34 #1444 | Zbl 0178.38802

[13] G. W. Mackey, Ergodic Theory and its Significance for Statistical Mechanics and Probability Theory (Advances in Math., Vol. 12, 1974, pp. 178-268). | MR 49 #10857 | Zbl 0326.60001

[14] C. C. Moore, Ergodicity of Flows on Homogeneous Spaces (Amer. J. Math., Vol. 88, 1966, pp. 154-178). | MR 33 #1409 | Zbl 0148.37902

[15] A. Ramsay, Virtual Groups and Group Actions (Advances in Math., Vol. 6, 1971, pp. 253-322). | MR 43 #7590 | Zbl 0216.14902

[16] C. Series, The Rohlin Theorem and Hyperfiniteness for Actions of Continuous Groups (to appear).

[17] V. S. Varadarajan, Geometry of Quantum Theory, Vol. II, van Nostrand, Princeton, N. J., 1970. | MR 57 #11400 | Zbl 0194.28802

[18] R. J. Zimmer, Extensions of Ergodic Group Actions (Illinois J. Math., Vol. 20, 1976, pp. 373-409). | MR 53 #13522 | Zbl 0334.28015

[19] R. J. Zimmer, Amenable Ergodic Actions, Hyperfinite Factors, and Poincaré Flows (Bull. Amer. Math. Soc., Vol. 83, 1977, pp. 1078-1080). | MR 57 #591 | Zbl 0378.28008

[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). | MR 57 #12775 | Zbl 0391.28011

[21] R. J. Zimmer, On the von Neumann Algebra of an Ergodic Group Action (Proc. Amer. Math. Soc., Vol. 66, 1977, pp. 289-293). | MR 57 #592 | Zbl 0367.28013

[22] R. J. Zimmer, Hyperfinite Factors and Amenable Ergodic Actions (Invent. Math., Vol. 41, 1977, pp. 23-31). | MR 57 #10438 | Zbl 0361.46061

[23] R. J. Zimmer, Amenable Pairs of Groups and Ergodic Actions and the Associated von Neumann Algebras [Trans. Amer. Math. Soc. (to appear)]. | Zbl 0408.22011

[24] R. J. Zimmer, Orbit Spaces of Unitary Representations, Ergodic Theory, and Simple Lie Groups (Ann. of Math., Vol. 106, 1977, pp. 573-588). | MR 57 #6286 | Zbl 0393.22006

[25] P. Hahn, The σ-Representations of Amenable Groupoids, preprint.