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arXiv · 1004.0072

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

Magnus Goffeng
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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.

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Magnus Goffeng. 2010-04-01. A remark on twists and the notion of torsion-free discrete quantum groups. https://arxiv.org/abs/1004.0072

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