SAT actions of discrete quantum groups and minimal injective extensions of their von Neumann algebras

2021/12/14 by Mehrdad Kalantar, Kalantar, Mehrdad, Fatemeh Khosravi +3
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2112.07206

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.

Related

• The unitary implementation of a locally compact quantum group action
• Idempotent states on locally compact groups and quantum groups
• Reiter's properties for the actions of locally compact quantum groups on von Neumann algebras
• Amenability and covariant injectivity of locally compact quantum groups
• Invariant subsets under compact quantum group actions