Twisting and Rieffel's deformation of locally compact quantum groups. Deformation of the Haar measure.

Pierre Fima (1) , Leonid Vainerman (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We develop the twisting construction for locally compact quantum groups. A new feature, in contrast to the previous work of M. Enock and the second author, is a non-trivial deformation of the Haar measure. Then we construct Rieffel's deformation of locally compact quantum groups and show that it is dual to the twisting. This allows to give new interesting concrete examples of locally compact quantum groups, in particular, deformations of the classical $az+b$ group and of the Woronowicz' quantum $az+b$ group.

Mots clés: Quantum groups; twisting; Rieffel's deformations

Domaines: Algèbres d'opérateurs [math.OA]

Pierre Fima, Leonid Vainerman. Twisting and Rieffel's deformation of locally compact quantum groups. Deformation of the Haar measure.. 2008. ⟨hal-00204131⟩