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

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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 Feldman-Sutherland-Zimmer ([<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), 993-1009, 2007-10-01

    The Mathematical Society of Japan

References:  23

Codes

  • NII Article ID (NAID)
    10019989259
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    9304048
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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