Algebry operatorów i ich zastosowania w fizyce

We characterise coideals of the algebra of functions on a locally compact quantum group G which are assigned to open subgroups by taking the quotient. We shall also extend (beyond coamenable case) Salmi's characterisation of coideals that are assigned to compact subgroups of G . Finally we relate open subgroups of G with a certain class of idempotent states on the dual of G. This is work in progress with F. Khosravi.