Gorenstein subrings of invariants under Hopf algebra actions

This paper concerns conditions on the action of a finite dimensional semisimple Hopf algebra on an Artin–Schelter regular algebra that force the subring of invariants to satisfy the Artin–Schelter Gorenstein condition. Classical results such as Watanabe's Theorem and Stanley's Theorem are extended from the case of a group action to the context of a Hopf algebra action. A Hopf algebra version of the homological determinant is introduced, and it becomes an important tool in the generalization from group actions to Hopf algebra actions.