A Galois correspondence for compact quantum group actions

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 $M^{\mathbb{G}}\subset M$.

18 pages

References in corpus (1)

• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups