Tracial central states on compact quantum groups

2024/07/27 by Freslon, Amaury, Skalski, Adam, Wang, Simeng · 1 citation
#46L67 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 20G42 #Quantum Algebra (math.QA) #Secondary 46L55

paper · doi:10.48550/arxiv.2407.19314

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.

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