You are here: Home :: Area NEM :: Mathematics

Stefaan Vaes

Strictly Outer Actions of Groups and Quantum Groups

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.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2005, 01/2005
Pages: 147 - 184

Show full article (external site)

Show all available items of this journal

 

Area NEM