Classification of Non-Kac compact quantum groups of SU(n) Type

Abstract

We classify up to isomorphism all non-Kac compact quantum groups with the same fusion rules and dimension function as SU(n). For this we first prove, using categorical Poisson boundary, the following general result. Let G be a coamenable compact quantum group and K be its maximal quantum subgroup of Kac type. Then any dimension-preserving unitary fiber functor RepG→Hilbf factors, uniquely up to isomorphism, through RepK. Equivalently, we have a canonical bijection H2(ˆG;T)≅H2(ˆK;T). Next, we classify autoequivalences of the representation categories of twisted q-deformations of compact simple Lie groups. The final version of this research has been published in International Mathematics Research Notices. © 2016 Oxford University Press