# Noncommutative Furstenberg boundary

@article{Kalantar2020NoncommutativeFB, title={Noncommutative Furstenberg boundary}, author={Mehrdad Kalantar and Paweł Kasprzak and Adam G. Skalski and Roland Vergnioux}, journal={arXiv: Operator Algebras}, year={2020} }

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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