On strongly graded Gorestein orders

Abstract

Let G be a finite group and let = g2G g be a strongly G-graded R-algebra, where R is a commutative ring with unity. We prove that if R is a Dedekind domain with quotient field K, is an R-order in a separable K-algebra such that the algebra 1 is a Gorenstein R-order, then is also a Gorenstein R-order. Moreover, we prove that the induction functor ind : Mod H ! Mod defined in Section 3, for a subgroup H of G, commutes with the standard duality functor