Abstract

Let R be a Noetherian PI connected graded Artin-Schelter regular do -main of GK-dimension d ≥ 2, and H be a semisimple Hopf algebra acting on R inner faithfully and homogeneously. Suppose that the homological determinant of the H-action is trivial. In this talk, we prove that, if the natural map φ : R#H → End _R^H (R), r#h → (x → r(h · x)) is injective, then it is also surjective.