Algebry operatorów i ich zastosowania w fizyce

The notion of an open quantum subgroup of a locally compact quantum group is introduced and given several equivalent characterisations in terms of group-like projections, inclusions of quantum group -algebras and properties of respective quantum homogenous spaces. Open quantum subgroups are shown to be closed in the sense of Vaes and normal open quantum subgroups are proved to be in 1-1 correspondence to compact quantum subgroups of the dual quantum group.(Joint work with Mehrdad Kalantar and Adam Skalski)