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A characterization of coactions whose fixed-point algebras contain special maximal abelian *-subalgebras
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)
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Submitter: 青井 久
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