On strongly graded Gorestein orders

Abstract

Let G be a finite group and let Λ = ⊕g∈GΛg 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, Λ is an R-order in a separable K-algebra such that the algebra Λ1 is a Gorenstein R-order, then Λ is also a Gorenstein R-order. Moreover, we prove that the induction functor ind : ModΛH → ModΛ defined in Section 3, for a subgroup H of G, commutes with the standard duality functor.