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Identities and isomorphisms of graded simple algebras |
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| Authors: | Plamen Koshlukov Mikhail Zaicev |
| Affiliation: | a Department of Mathematics, IMECC, UNICAMP, P.O. Box 6065, 13083-970 Campinas, SP, Brazil b Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow 119992, Russia |
| Abstract: | 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. |
| Keywords: | Graded simple algebras Gradings on associative algebras Graded division algebras Graded isomorphisms Graded identities Polynomial identities |
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