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