A Galois correspondence for compact quantum group actions

TL;DR

This paper extends the Galois correspondence to minimal actions of compact quantum groups on von Neumann factors, establishing a one-to-one link between coideals and intermediate subfactors, generalizing prior Kac algebra results.

Contribution

It generalizes the Galois correspondence from Kac algebras to all compact quantum groups acting on von Neumann factors.

Findings

Established a bijective correspondence between coideals and subfactors.

Extended previous results from Kac algebra case to general compact quantum groups.

Provides a framework for understanding symmetries in operator algebras.

Abstract

We establish a Galois correspondence for a minimal action of a compact quantum group ${\mathbb G}$ on a von Neumann factor $M$. This extends the result of Izumi, Longo and Popa who treated the case of a Kac algebra. Namely, there exists a one-to-one correspondence between the lattice of left coideals of ${\mathbb G}$ and that of intermediate subfactors of $M^{\mathbb G}\subset M$.