Sidon sets for compact quantum groups

Simeng Wang

Published 2015-07-05Version 1

This paper is devoted to the study of Sidon sets and some related objects for compact quantum groups. We establish the equivalence between several different characterizations of Sidon sets for compact quantum groups, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets and $\Lambda(p)$-sets, generalizing a previous work by Blendek and Michali\u{c}ek. We also prove the existence of $\Lambda(p)$-sets for orthogonal systems for noncommutative $L^p$-spaces, and deduce the corresponding properties for compact quantum groups. Some basic properties of central Sidon sets are discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also studied.