Central Invariants of H-module algebras

Let H be a Hopf algebra over a field k, and A an H-module algebra, with subalgebra of H-invariants denoted by A^H. When (H, R) is quasitriangular and A is quantum commutative with respect to (H, R), (e.g. quantum planes, graded commutative superalgebras), then [formula ommitted] center of A =Z(A). In this paper we are mainly concerned with actions of H for which A^H⊂ Z(A). We show that under this hypothesis there exists strong relations between the ideal structures of A^H, A and A#H. We demonstrate the theorems by constructing an example of a quantum commutative A, so that A/A^His H*-Galois. This is done by giving (C G)*, G = Z_n X Z_n,a nontrivial quasitriangular structure and defining an action of it on a localization of the quantum plane.