Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter July 27, 2005

Strictly Outer Actions of Groups and Quantum Groups

  • Stefaan Vaes

Abstract

An action of a locally compact group or quantum group on a factor is said to be strictly outer when the relative commutant of the factor in the crossed product is trivial. We show that all locally compact quantum groups can act strictly outerly on a free Araki-Woods factor and that all locally compact groups can act strictly outerly on the hyperfinite II1 factor. We define a kind of Connes' T invariant for locally compact quantum groups and prove a link with the possibility of acting strictly outerly on a factor with a given T invariant. Necessary and sufficient conditions for the existence of strictly outer actions of compact Kac algebras on the hyperfinite II1 factor are given.

:
Published Online: 2005-07-27
Published in Print: 2005-01-01

© Walter de Gruyter

Downloaded on 29.3.2024 from https://www.degruyter.com/document/doi/10.1515/crll.2005.2005.578.147/html
Scroll to top button