Algebry operatorów i ich zastosowania w fizyce

The quantized universal enveloping algebra of a semisimple Lie group admits an extension by a tuple of group-like central elements. Specializations with respect to tuples in the center of the compact form provides twisted tensor category of representations of the q-deformation quantum group. We investigate the compact quantum group realization of this construction. For the case of SUq(n) quantum groups, we obtain the quantum group realization of the twisted tensor category which appear in the classification by Kazhdan and Wenzl. Based on a joint work with Sergey Neshveyev.