Identities and isomorphisms of graded simple algebras

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Let G be an arbitrary abelian group and let A and B be two finite dimensional G-graded simple algebras over an algebraically closed field F such that the orders of all finite subgroups of G are invertible in F. We prove that A and B are isomorphic if and only if they satisfy the same G-graded identities. We also describe all isomorphism classes of finite dimensional G-graded simple algebras. (C) 2010 Elsevier Inc. All rights reserved.4321231413148Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)RFBR [09-01-00303, SSC-1983.2008.1]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [302651/2008-0]FAPESP [05/60337-2, 2008/02938-8]RFBR [09-01-00303, SSC-1983.2008.1