Towards a quantum galois theory for quantum double algebras of finite groups

Suppose that G is a finite group and D(G) the quantum double algebra of G. Let A be the field algebra of G-spin models. There is a natural action of D(G) on A such that A becomes a D(G)-module algebra. For a subgroup H of G, there is a Hopf subalgebra D(G;H) of D(G). Based on the concrete construction of a D(G;H) fixed point subalgebra, the paper proves that D(G;H) is Galois closed and thus gives a quantum Galois theory in the field algebra of G-spin models.