Algebry operatorów i ich zastosowania w fizyce

The notion of the Hopf center and Hopf cocenter of a Hopf algebra isinvestigated using the extension theory of Hopf algebras. We prove thateach of them yields an exact sequence of Hopf algebras. Moreover, the exact sequences are shown to satisfy the faithful (co)flatness condition.The Hopf center and cocenter are computed for the quantized universalenveloping algebra of a simple complex Lie algebra and for the Hopf algebra of the Drinfeld-Jimbo quantization of a compact semisimple simply connected Lie group. Joint work with Alexandru Chirvasitu.In this second part of the talk I will be focused on the concept of a Hopf cocenter.