ON GORENSTEINNESS OF HOPF MODULE ALGEBRAS. (10th June 2016) - SKRYABIN, SERGE
Abstract: Let H be a Hopf algebra with a bijective antipode, A an H -simple H -module algebra finitely generated as an algebra over the ground field and module-finite over its centre. The main result states that A has finite injective dimension and is, moreover, Artin–Schelter Gorenstein under the additional assumption that each H -orbit in the space of maximal ideals of A is dense with respect to the Zariski topology. Further conclusions are derived in the cases when the maximal spectrum of A is a single H -orbit or contains an open dense H -orbit.