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Duality for Actions and Coactions of Measured Groupoids on Von Neumann Algebras

Duality for Actions and Coactions of Measured Groupoids on Von Neumann Algebras (Paperback)

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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.

Science & MathematicsMathematicsGroups & group theory Publisher: American Mathematical Society Publication Date: 15/01/1993 ISBN-13: 9780821825457  Details: Type: Paperback Format: Books
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