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Orbital factor map

Published online by Cambridge University Press:  19 September 2008

Toshihiro Hamachi  and
Hideki Kosaki
Toshihiro Hamachi
Affiliation:
Department of Mathematics, College of General Education, Kyushu University, Ropponmatsu, Chuo-ku, Fukuoka, 810, Japan
Hideki Kosaki
Affiliation:
Department of Mathematics, College of General Education, Kyushu University, Ropponmatsu, Chuo-ku, Fukuoka, 810, Japan
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Abstract

For a certain pair of discrete measured ergodic equivalence relations, we specify how one is imbedded into the other and obtain a factor and its subfactor. For this pair of factors index theory is developed. We obtain an index formula, an ‘extended’ relation corresponding to the basic extension, and so on. Our formulas as well as construction are very explicit and are given in terms of ‘measure theoretic’ data. We also present examples showing the contrast between type III0 index theory and type II1 (or IIIλ) index theory.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 3 , September 1993 , pp. 515 - 532
Copyright
Copyright © Cambridge University Press 1993

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