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 $\mathcal A$ be the field algebra of $G$-spin models. There is a natural action of $D(G)$ on $\mathcal A$ such that $\mathcal A$ 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.