Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Quasinormal subrelations of ergodic
equivalence relations

Author: Alexandre I. Danilenko
Journal: Proc. Amer. Math. Soc. 126 (1998), 3361-3370
MSC (1991): Primary 28D99, 46L55
MathSciNet review: 1610944
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a notion of quasinormality for a nested pair $\mathcal{S}\subset \mathcal{R}$ of ergodic discrete hyperfinite equivalence relations of type $II_{1}$. (This is a natural extension of the normality concept due to Feldman-Sutherland-Zimmer.) Such pairs are characterized by an irreducible pair $F\subset Q$ of countable amenable groups or rather (some special) their Polish closure $\overline{F}\subset \overline{Q}$. We show that ``most'' of the ergodic subrelations of $\mathcal{R}$ are quasinormal and classify them. An example of a nonquasinormal subrelation is given. We prove as an auxiliary statement that two cocycles of $\mathcal{R}$ with dense ranges in a Polish group are weakly equivalent.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28D99, 46L55

Retrieve articles in all journals with MSC (1991): 28D99, 46L55

Additional Information

Alexandre I. Danilenko
Affiliation: Department of Mechanics and Mathematics, Kharkov State University, Freedom square 4, Kharkov, 310077, Ukraine

Received by editor(s): April 10, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society