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

Aoi, Hisashi; Yamanouchi, Takehiko

Ergodic Theory and Dynamical Systems, 2006, 26(6), 1673-1706

Permalink : https://hdl.handle.net/2115/18641

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アクセス権	open access
URI	https://hdl.handle.net/2115/18641
タイトル	A characterization of coactions whose fixed-point algebras contain special maximal abelian *-subalgebras
著者	著者名 Aoi, Hisashi
著者	著者名 Yamanouchi, Takehiko
言語	英語
発行日	2006
出版者	Cambridge University Press
収録物名	Ergodic Theory and Dynamical Systems
巻(号)	26(6)
ページ	1673-1706
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
権利情報	Copyright © 2006 Cambridge University Press
PISSN	0143-3857
EISSN	1469-4417
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1017/S0143385706000459