# zbMATH — the first resource for mathematics

Ergodic equivalence relations, cohomology, and von Neumann algebras. I. (English) Zbl 0369.22009

##### MSC:
 22D40 Ergodic theory on groups 28D05 Measure-preserving transformations 20Jxx Connections of group theory with homological algebra and category theory 22D25 $$C^*$$-algebras and $$W^*$$-algebras in relation to group representations 46L10 General theory of von Neumann algebras 18G99 Homological algebra in category theory, derived categories and functors
Full Text:
##### References:
 [1] Warren Ambrose, Representation of ergodic flows, Ann. of Math. (2) 42 (1941), 723 – 739. · Zbl 0025.26901 [2] Hirotada Anzai, Ergodic skew product transformations on the torus, Osaka Math. J. 3 (1951), 83 – 99. · Zbl 0043.11203 [3] Louis Auslander and Calvin C. Moore, Unitary representations of solvable Lie groups, Mem. Amer. Math. Soc. No. 62 (1966), 199. · Zbl 0204.14202 [4] Alain Connes, Une classification des facteurs de type \?\?\?, Ann. Sci. École Norm. Sup. (4) 6 (1973), 133 – 252 (French). · Zbl 0274.46050 [5] Alain Connes and M. Takesaki, Flots des poids sur les facteurs de type \?\?\?, C. R. Acad. Sci. Paris Sér. A 278 (1974), 945 – 948 (French). · Zbl 0274.46051 [6] -[2], The flow of weights on a factor of type III (preprint). [7] Dang Ngoc Nghiem, On the classification of dynamical systems, Ann. Inst. H. Poincaré Sect. B (N.S.) 9 (1973), 397 – 425. · Zbl 0278.58009 [8] H. A. Dye, On groups of measure preserving transformation. I, Amer. J. Math. 81 (1959), 119 – 159. · Zbl 0087.11501 [9] H. A. Dye, On groups of measure preserving transformations. II, Amer. J. Math. 85 (1963), 551 – 576. · Zbl 0191.42803 [10] Eilenberg and S. Mac Lane [1], Cohomology theory in abstract groups. I, Ann. of Math. (2) 48 (1947), 51-78. MR 8, 367. · Zbl 0029.34001 [11] J. Feldman and D. A. Lind, Hyperfiniteness and the Halmos-Rohlin theorem for nonsingular Abelian actions, Proc. Amer. Math. Soc. 55 (1976), no. 2, 339 – 344. · Zbl 0302.46047 [12] Jacob Feldman and Calvin C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras, Bull. Amer. Math. Soc. 81 (1975), no. 5, 921 – 924. · Zbl 0317.22002 [13] J. M. G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472 – 476. · Zbl 0106.15801 [14] Toshihiro Hamachi, Yukimasa Oka, and Motosige Osikawa, Flows associated with ergodic non-singular transformation groups, Publ. Res. Inst. Math. Sci. 11 (1975/76), no. 1, 31 – 50. · Zbl 0316.28007 [15] Shizuo Kakutani, Induced measure preserving transformations, Proc. Imp. Acad. Tokyo 19 (1943), 635 – 641. · Zbl 0060.27406 [16] A. Krieger [1], On non-singular transformations of a measure space. I, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete. 11 (1969), 83-97. MR 39 # 1628. · Zbl 0185.11901 [17] Wolfgang Krieger, On non-singular transformations of a measure space. I, II, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 11 (1969), 83-97; ibid. 11 (1969), 98 – 119. · Zbl 0185.11901 [18] Wolfgang Krieger, On constructing non-*isomorphic hyperfinite factors of type III, J. Functional Analysis 6 (1970), 97 – 109. · Zbl 0209.44601 [19] Wolfgang Krieger, On a class of hyperfinite factors that arise from null-recurrent Markov chains, J. Functional Analysis 7 (1971), 27 – 42. · Zbl 0215.25901 [20] Wolfgang Krieger, On the Araki-Woods asymptotic ratio set and non-singular transformations of a measure space, Contributions to Ergodic Theory and Probability (Proc. Conf., Ohio State Univ., Columbus, Ohio, 1970) Springer, Berlin, 1970, pp. 158 – 177. Lecture Notes in Math., Vol. 160. [21] Wolfgang Krieger, On ergodic flows and the isomorphism of factors, Math. Ann. 223 (1976), no. 1, 19 – 70. · Zbl 0332.46045 [22] Kuratowski [1], Topologie, Warsaw-Livoue, 1933. · JFM 59.0563.02 [23] George W. Mackey, Point realizations of transformation groups, Illinois J. Math. 6 (1962), 327 – 335. · Zbl 0178.17203 [24] George W. Mackey, Ergodic theory and virtual groups, Math. Ann. 166 (1966), 187 – 207. · Zbl 0178.38802 [25] Calvin C. Moore, Extensions and low dimensional cohomology theory of locally compact groups. I, II, Trans. Amer. Math. Soc. 113 (1964), 40 – 63. · Zbl 0131.26902 [26] -[2], Extensions and low dimensional cohomology theory of locally compact groups. II, Trans. Amer. Math. Soc. 113 (1964), 64-86. MR 30 #2106. · Zbl 0131.26902 [27] Calvin C. Moore, Group extensions and cohomology for locally compact groups. III, Trans. Amer. Math. Soc. 221 (1976), no. 1, 1 – 33. · Zbl 0366.22005 [28] Calvin C. Moore, Group extensions and cohomology for locally compact groups. IV, Trans. Amer. Math. Soc. 221 (1976), no. 1, 35 – 58. · Zbl 0366.22006 [29] Joseph Max Rosenblatt, Equivalent invariant measures, Israel J. Math. 17 (1974), 261 – 270. · Zbl 0286.28014 [30] Shôichirô Sakai, \?*-algebras and \?*-algebras, Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60. · Zbl 0233.46074 [31] Schmidt [1], Cohomology and skew products of ergodic transformations, Warwick, 1974 (preprint). [32] Joel J. Westman, Cohomology for the ergodic actions of countable groups, Proc. Amer. Math. Soc. 30 (1971), 318 – 320. · Zbl 0229.28012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.