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October, 2007 Normality for an inclusion of ergodic discrete measured equivalence relations in the von Neumann algebraic framework
Takehiko YAMANOUCHI
J. Math. Soc. Japan 59(4): 993-1009 (October, 2007). DOI: 10.2969/jmsj/05940993

Abstract

It is shown that for the inclusion of factors ( B A ) : = ( W * ( S , ω ) W * ( R , ω ) ) corresponding to an inclusion of ergodic discrete measured equivalence relations S R , S is normal in R in the sense of Feldman-Sutherland-Zimmer ([9]) if and only if A is generated by the normalizing groupoid of B . Though this fact has been already obtained in [3], we reprove it here by a quite different method.

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Takehiko YAMANOUCHI. "Normality for an inclusion of ergodic discrete measured equivalence relations in the von Neumann algebraic framework." J. Math. Soc. Japan 59 (4) 993 - 1009, October, 2007. https://doi.org/10.2969/jmsj/05940993

Information

Published: October, 2007
First available in Project Euclid: 10 December 2007

zbMATH: 1136.46046
MathSciNet: MR2370002
Digital Object Identifier: 10.2969/jmsj/05940993

Subjects:
Primary: 46L55
Secondary: 28D99

Keywords: (normal) subrelation , basic extension , group coaction , measured equivalence relation

Rights: Copyright © 2007 Mathematical Society of Japan

Vol.59 • No. 4 • October, 2007
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