Abstract
Let H be a finite dimensional, semisimple Hopf algebra over a field K and let A be an H- module algebra. Assume K is a splitting field for H and that H is strongly semiprime. If A is H- semiprime, we show the Connes spectrum of H acting on A consists of all of the irreducible representations of H is equivalent to every nonzero annihilator ideal of the smash product meets A nontrivially. If H is also cocommutative, we let I′ be the intersection of the annihilators of the modules in the Connes spectrum. We find some of the information encoded in the Hopf kernel of the natural map from H to H/I′.
1991 Mathematics Subject Classafication.: