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Duality for Actions and Coactions of Measured Groupoids on von Neumann Algebras
Takehiko Yamanouchi

Memoirs of the American Mathematical Society
1993; 109 pp; softcover
Volume: 101
ISBN-10: 0-8218-2545-3
ISBN-13: 978-0-8218-2545-7
List Price: US$31
Individual Members: US$18.60
Institutional Members: US$24.80
Order Code: MEMO/101/484
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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.


Research mathematicians.

Table of Contents

  • 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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