An Ideal Correspondence Result for Crossed Products by Quantum Groups

Given a weak Kac system with duality arising from a regular quantum group, we construct natural lattice isomorphisms from the coaction invariant ideals of a C* algebra coacted on by such a quantum group, and the dual coaction invariant ideals of the full and reduced crossed products.  We represent clearer conventions, give motivating examples, and explain the conventions we used (primarily of Baaj and Skandalis) and how they connect to the conventions of Kustermans and Vaes.