Simple 𝐺-graded algebras and their polynomial identities

Abstract

Let G G be any group and F F an algebraically closed field of characteristic zero. We show that any G G -graded finite dimensional associative G G -simple algebra over F F is determined up to a G G -graded isomorphism by its G G -graded polynomial identities. This result was proved by Koshlukov and Zaicev in case G G is abelian.