Cohomology groups, multipliers and factors in ergodic theory

• Autorzy: M. Lemańczyk
• Języki publikacji: EN

Abstrakty

EN

The problem of compact factors in ergodic theory and its relationship with the problem of extending a cocycle to a cocycle of a larger action are studied.

Kategorie tematyczne

• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 3
• Strony: 275-288

Daty

wydano

1997

otrzymano

1995-12-11

poprawiono

1996-08-28

Twórcy

autor

M. Lemańczyk

• Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] V. Bargman, On unitary ray representations of continuous groups, Ann. of Math. 59 (1954), 1-46.
• [2] A. I. Danilenko, Comparison of cocycles of a measured equivalence relation and lifting problems, Ergodic Theory Dynam. Systems, to appear.
• [3] P. Gabriel, M. Lemańczyk and K. Schmidt, Extensions of cocycles for hyperfinite actions, and applications, Monatsh. Math. (1996), to appear.
• [4] A. del Junco, M. Lemańczyk and M. K. Mentzen, Semisimplicity, joinings and group extensions, Studia Math. 112 (1995), 141-164.
• [5] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynam. Systems 7 (1987), 531-557.
• [6] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. 13 (1965), 397-403.
• [7] J. Kwiatkowski, Factors of ergodic group extensions of rotations, Studia Math. 103 (1992), 123-131.
• [8] M. Lemańczyk, Ergodic Compact Abelian Group Extensions of Rotations, Publ. N. Copernicus University, 1990 (habilitation).
• [9] 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 Dynam. Systems 10 (1990), 763-776.
• [10] G. W. Mackey, Borel structures in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134-169.
• [11] M. K. Mentzen, Ergodic properties of group extensions of dynamical systems with discrete spectra, Studia Math. 101 (1991), 19-31.
• [12] C. C. Moore and K. Schmidt, Coboundaries and homomorphisms for non-singular actions and a problem of H. Helson, Proc. London Math. Soc. 40 (1980), 443-475.
• [13] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136.
• [14] K. R. Parthasarathy, Multipliers on Locally Compact Groups, Lecture Notes in Math. 93, Springer, 1969.
• [15] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, Mac Millan of India, 1977.
• [16] J.-P. Thouvenot, Some properties and applications of joinings in ergodic theory, in: Ergodic Theory and its Connections with Harmonic Analysis, London Math. Soc., 1995, 207-235.
• [17] W. A. Veech, A criterion for a process to be prime, Monatsh. Math. 94 (1982), 335-341.