Duality for actions and coactions of measured groupoids of von Neumann algebras
著者
書誌事項
Duality for actions and coactions of measured groupoids of von Neumann algebras
（Memoirs of the American Mathematical Society, no. 484）
American Mathematical Society, 1993
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注記
Includes bibliographical references (p. 106-109)
"January 1993, volume 101, number 484 (third of 4 numbers)" -- T.p
内容説明・目次
内容説明
Through classification of compact abelian group actions on semifinite injective factors, Jones and Takesaki introduced the notion of an action of a measured groupoid on a von Neumann algebra, which has proven to be an important tool for this kind of analysis. Elaborating on this notion, this work introduces a new concept of a measured groupoid action that may fit more perfectly into the groupoid setting. Yamanouchi also shows the existence of a canonical coproduct on every groupoid von Neumann algebra, which leads to a concept of a coaction of a measured groupoid. Yamanouchi then proves duality between these objects, extending Nakagami-Takesaki duality for (co)actions of locally compact groups on von Neumann algebras.
目次
Relative tensor products of Hilbert spaces over abelian von Neumann algebras Coproducts of groupoid von Neumann algebras Actions and coactions of measured groupoids on von Neumann algebras Crossed products by groupoid actions and their dual coactions Crossed products by groupoid coactions and their dual actions Duality for actions on von Neumann algebras Duality for integrable coactions on von Neumann algebras Examples of actions and coactions of measured groupoids on von Neumann algebras.
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