• Corpus ID: 211259207

Noncommutative Furstenberg boundary

  title={Noncommutative Furstenberg boundary},
  author={Mehrdad Kalantar and Paweł Kasprzak and Adam G. Skalski and Roland Vergnioux},
  journal={arXiv: Operator Algebras},
We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete quantum group. As for classical groups, properties of boundary actions turn out to encode significant properties of the operator algebras associated with the discrete quantum group in question; for example we prove that if the action on the Furstenberg boundary is faithful, the quantum group C*-algebra admits at most one KMS-state for the scaling automorphism group. To obtain these results we… 
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