Download or read book Duality for Actions and Coactions of Measured Groupoids of Von Neumann Algebras written by Takehiko Yamanouchi and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.