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

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

2008-01-12

arxiv.org/abs/0801.1906v1

Mathematics

Operator Algebras

Scientific paper

10.1007/s00220-008-0559-5

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.

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