Classification of Idempotent States on the compact quantum groups U_q(2), SU_q(2), and SO_q(3) - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

Classification of Idempotent States on the compact quantum groups U_q(2), SU_q(2), and SO_q(3)

Uwe Franz
Adam Skalski
  • Fonction : Auteur
Reiji Tomatsu
  • Fonction : Auteur

Résumé

We give a simple characterisation of those idempotent states on compact quantum groups which arise as Haar states on quantum subgroups, show that all idempotent states on quantum groups U_q(2), SU_q(2), and SO_q(3) (q in (-1,1] \ {0}) arise in this manner and list the idempotent states on compact quantum semigroups U_0(2), SU_0(2), and SO_0(3). In the Appendix we provide a simple proof of coamenability of the deformations of classical compact Lie groups.

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hal-00470204 , version 1 (05-04-2010)

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Uwe Franz, Adam Skalski, Reiji Tomatsu. Classification of Idempotent States on the compact quantum groups U_q(2), SU_q(2), and SO_q(3). 2009. ⟨hal-00470204⟩
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