SAT ACTIONS OF DISCRETE QUANTUM GROUPS AND MINIMAL INJECTIVE EXTENSIONS OF THEIR VON NEUMANN ALGEBRAS

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. © 2024 American Mathematical Society.