Duality for actions and coactions of measured groupoids of von Neumann algebras / Takehiko Yamanouchi.

Format:

Book

Author/Creator:

Yamanouchi, Takehiko, 1961- author.

Series:

Memoirs of the American Mathematical Society ; Volume 101, Number 484.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 101, Number 484

Language:

English

Subjects (All):

Von Neumann algebras.

Groupoids.

Duality theory (Mathematics).

Physical Description:

1 online resource (122 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1993.

Language Note:

English

Summary:

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.

Contents:

""Table of Contents""; ""Abstract""; ""Â 0. Introduction""; ""Â 1. Relative tensor products of Hilbert spaces over abelian von Neumann algebras""; ""Â 2. Coproducts of groupoid von Neumann algebras""; ""Â 3. Actions and coactions of measured groupoids on von Neumann algebras""; ""Â 4. Crossed products by groupoid actions and their dual coactions""; ""Â 5. Crossed products by groupoid coactions and their dual actions""; ""Â 6. Duality for actions on von Neumann algebras""; ""Â 7. Duality for integrable coactions on von Neumann algebras""

""Â 8. Examples of actions and coactions of measured groupoids on von Neumann algebras""""References""

Notes:

"January 1993, Volume 101, Number 484 (third of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0061-8