CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

A Note on Uniformly Bounded Cocycles into Finite von Neumann Algebras

  Published:2018-01-17
 Printed: Jun 2018
  • Remi Boutonnet,
    Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 Cours de la Libération, 33405 Talence Cedex, France
  • Jean Roydor,
    Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 Cours de la Libération, 33405 Talence Cedex, France
Format:   LaTeX   MathJax   PDF  

Abstract

We give a short proof of a result of T. Bates and T. Giordano stating that any uniformly bounded Borel cocycle into a finite von Neumann algebra is cohomologous to a unitary cocycle. We also point out a separability issue in their proof. Our approach is based on the existence of a non-positive curvature metric on the positive cone of a finite von Neumann algebra.
Keywords: Borel cocycle, von Neumann algebra Borel cocycle, von Neumann algebra
MSC Classifications: 46L55, 46L40, 22D40 show english descriptions Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
Automorphisms
Ergodic theory on groups [See also 28Dxx]
46L55 - Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
46L40 - Automorphisms
22D40 - Ergodic theory on groups [See also 28Dxx]
 

© Canadian Mathematical Society, 2018 : https://cms.math.ca/