Algebry operatorów i ich zastosowania w fizyce

Department of Mathematical Methods in Physics In this talk I will present several recent results on Sidon sets for (quantum) groups. I will establish the equivalence between several different characterizations of Sidon sets for compact quantum groups, and in particular prove that in a discrete group the notions of Sidon sets and strong Sidon sets in the sense of Picardello coincide. I will also prove that any Sidon set for a compact quantum group is a \Lambda(p)-set for a finite p, generalizing previous results of Blendek and Michalicek. Some basic properties of central lacunarity will be also discussed - I will show that in the contrast to the classical SU(2) case one can exhibit a central \Lambda(4)-set for the quantum group SU_q(2). Finally on the other hand I will also prove that the Drinfeld-Jimbo deformations of simply connected compact semi-simple Lie groups (so for example SU_q(2)) do not admit infinite Sidon sets.

In this talk I will present several recent results on Sidon sets for (quantum) groups. I will establish the equivalence between several different characterizations of Sidon sets for compact quantum groups, and in particular prove that in a discrete group the notions of Sidon sets and strong Sidon sets in the sense of Picardello coincide. I will also prove that any Sidon set for a compact quantum group is a \Lambda(p)-set for a finite p, generalizing previous results of Blendek and Michalicek. Some basic properties of central lacunarity will be also discussed - I will show that in the contrast to the classical SU(2) case one can exhibit a central \Lambda(4)-set for the quantum group SU_q(2). Finally on the other hand I will also prove that the Drinfeld-Jimbo deformations of simply connected compact semi-simple Lie groups (so for example SU_q(2)) do not admit infinite Sidon sets.