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A characterization of coactions whose fixed-point algebras contain special maximal abelian *-subalgebras

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Title: A characterization of coactions whose fixed-point algebras contain special maximal abelian *-subalgebras
Authors: Aoi, Hisashi Browse this author
Yamanouchi, Takehiko Browse this author
Issue Date: 2006
Publisher: Cambridge University Press
Journal Title: Ergodic Theory and Dynamical Systems
Volume: 26
Issue: 6
Start Page: 1673
End Page: 1706
Publisher DOI: 10.1017/S0143385706000459
Abstract: It is shown that, for the von Neumann algebra A obtained from a principal measured groupoidRwith the diagonal subalgebraD of A, there exists a natural ‘bijective’ correspondence between coactions on A that fix D pointwise and Borel 1-cocycles on R. As an application of this result, we classify a certain type of coactions on approximately finite-dimensional type II factors up to cocycle conjugacy. By using our characterization of coactions mentioned above, we are also able to generalize to some extent those results of Zimmer concerning 1-cocycles on ergodic equivalence relations into compact groups.
Rights: Copyright © 2006 Cambridge University Press
Type: article
URI: http://hdl.handle.net/2115/18641
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 青井 久

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