SAT actions of discrete quantum groups and minimal injective extensions of their von Neumann algebras (2112.07206v2)

Published 14 Dec 2021 in math.OA and math.QA

Abstract: We introduce a natural generalization of the notion of strongly approximately transitive (SAT) states for actions of locally compact quantum groups. In the case of discrete quantum groups of Kac type, we show that the existence of unique stationary SAT states entails rigidity results concerning injective extensions of quantum group von Neumann algebras.

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