Identities and isomorphisms of finite-dimensional graded simple algebras

摘要

Let F be an algebraically closed field, G be an abelian group, and let U and V be arbitrary finite-dimensional G-graded simple algebras over F. We prove that U and V are isomorphic as graded algebras if, and only if, they satisfy the same graded polynomial identities. (C) 2019 Elsevier Inc. All rights reserved.