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Generic Results for Cocycles with Values in a Semidirect Product

Published online by Cambridge University Press:  20 November 2018

Karma Dajani
Karma Dajani*
Affiliation:
University of North Carolina, Chapel Hill, North Carolina 27599-3250
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Abstract

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Let A α B be the semidirect product of two local compact Hausdorff topological groups. We prove that for a nonsingularergodic automorphism T of a Lebesgue probability space, a generic cocycle taking values in A α B is nontrivial and recurrent.

Keywords

28A0528C10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 3 , 01 June 1993 , pp. 497 - 516
Copyright
Copyright © Canadian Mathematical Society 1993

References

[CHP] Choksi, J. R., Hawkins, J. M. and Prasad, V. S., Abelian cocyclesfor nonsingular transformations and genericity of type III1 transformations, Mh. Math. 102(1987), 187–205.Google Scholar
[D] Dajani, D. G., Genericity of nontrivial H-superrecurrentH-cocycles, Trans. Amer. Math. Soc. 323(1991), 111–132.Google Scholar
[HO] Hamachi, T. and Osikawa, M., Ergodic groups of automorphisms and Krieger's Theorem, Sem. Math. Sci. 3(1981).Google Scholar
[K] Krieger, W., On the Araka-Wood asymptotic ratio set and nonsingular transformations of a measure space, Contributions to ergodic theory and probability, Lect. Notes Math. 160(1970), 158–177.Google Scholar
[MF] Moore, C. and Feldman, J., Ergodic equivalence relations, cohomology and von Neumann algebras I, Trans. Amer. Soc. 234(1977), 289–324.Google Scholar
[PS] Parthasarathy, K. R. and Schmidt, K., On the cohomology of hyperfinite action, Mh. Math. 84( 1977), 37–48.Google Scholar
[SI] Schmidt, K., Cocycles of ergodic transformation group,MacMiMan Lectures in Math. New Delhi: MacMillan, India, (1977).Google Scholar
[S2] Schmidt, K., On Recurrence, Z. Wahrscheinlichkeitstheorie verw. Geb. 68(1984), 75–95.Google Scholar
[S3] Schmidt, K., Algebraic Ideas in Ergodic Theory, AMS Regional Conference Series in Math. 76(1990).Google Scholar
[Z] Zimmer, R. J., Ergodic theory and semisimple groups, Monographs in Math., Birkhàuser, (1984).Google Scholar