A remark on twists and the notion of torsion-free discrete quantum groups

Abstract

In this paper twists of reduced locally compact quantum groups are studied. Twists of the dual coaction on a reduced crossed product are introduced and the twisted dual coactions are proved to satisfy a type of Takesaki-Takai duality. The twisted Takesaki-Takai duality implies that twists of discrete, torsion-free quantum groups are torsion-free. Cocycle twists of duals of semisimple, compact Lie are studied leading to a locally compact quantum group contained in the Drinfeld-Jimbo algebra which gives a dual notion of Woronowicz deformations for semisimple, compact Lie groups. These cocycle twists are proven to be torsion-free whenever the Lie group is simply connected.

17 pages, to appear in Algebras and Representation Theory, http://www.springerlink.com/content/u33rr720672598r3/

References in corpus (3)

• The Baum-Connes conjecture for free orthogonal quantum groups
• Homological algebra in bivariant K-theory and other triangulated categories
• Galois objects and cocycle twisting for locally compact quantum groups