Tracial central states on compact quantum groups

TL;DR

This paper classifies tracial central states on universal C*-algebras of various compact quantum groups, extending classical concepts to quantum settings and providing a comprehensive understanding of their invariant states.

Contribution

It provides a complete classification of tracial central states on several classes of quantum groups, including q-deformations and free quantum groups, advancing the understanding of their invariant states.

Findings

Classified tracial central states on q-deformed compact Lie groups

Classified tracial central states on free orthogonal quantum groups

Classified tracial central states on quantum permutation and hyperoctahedral groups

Abstract

Motivated by classical investigation of conjugation invariant positive-definite functions on discrete groups, we study tracial central states on universal C*-algebras associated with compact quantum groups, where centrality is understood in the sense of invariance under the adjoint action. We fully classify such states on q-deformations of compact Lie groups, on free orthogonal quantum groups, quantum permutation groups and on quantum hyperoctahedral groups.