Normality for an inclusion of ergodic discrete measured equivalence relations in the von Neumann algebraic framework

 Yamanouchi Takehiko YAMANOUCHI Takehiko
 Department of Mathematics Faculty of Science Hokkaido University
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Author(s)

 Yamanouchi Takehiko YAMANOUCHI Takehiko
 Department of Mathematics Faculty of Science Hokkaido University
Abstract
It is shown that for the inclusion of factors (<I>B</I>⊆<I>A</I>):=(<I>W</I><SUP>*</SUP>(\\mathcal{S},ω)⊆<I>W</I><SUP>*</SUP>(\\mathcal{R},ω)) corresponding to an inclusion of ergodic discrete measured equivalence relations \\mathcal{S}⊆\\mathcal{R}, \\mathcal{S} is normal in \\mathcal{R} in the sense of FeldmanSutherlandZimmer ([<B>9</B>]) if and only if <I>A</I> is generated by the normalizing groupoid of <I>B</I>. Though this fact has been already obtained in [<B>3</B>], we reprove it here by a quite different method.
Journal

 Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 59(4), 9931009, 20071001
The Mathematical Society of Japan
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