  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.

Quantum Algebra;Operator Algebras