Fixed Points of Compact Quantum Groups Actions on Cuntz Algebras

@article{Gabriel2012FixedPO,
  title={Fixed Points of Compact Quantum Groups Actions on Cuntz Algebras},
  author={Olivier Gabriel},
  journal={Annales Henri Poincar{\'e}},
  year={2012},
  volume={15},
  pages={1013-1036}
}
Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results. Under certain conditions, we prove that the fixed point algebra is purely infinite and simple. We further identify it as a C*-algebra, compute its K-theory and prove a “stability property”: the fixed points only depend on the CQG via its fusion rules. We apply… 

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