Algebry operatorów i ich zastosowania w fizyce

In this talk I will discuss Hopf and C*-algebraic aspects of the theory of quantum groups with projection. On the Hopf level I will describe the Hopf algebra decomposition into the image of the projection and the sub-algebra of invariants, the former being a Hopf algebra whereas the later is a Hopf algebra in the braided sense. On the C*-level I will discuss the multiplicative unitary decomposition assigned to a projection.