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Let R s [ R be a G-graded ring. We describe all types of gradings on R ifG is torsion free and R is Artinian semisimple. If R is a matrix algebra over an algebraically closed field F, then we give a description of all G-gradings on R provided that G is an abelian group. In the case of an abelian group G we also classify all finite-dimensional graded simple algebras and finite-dimensional graded division algebras over an algebraically closed field of characteristic zero. ᮊ 2001Academic Press

In this paper we describe all group gradings by a finite Abelian group G of several types of simple Jordan and Lie algebras over an algebraically closed field F of characteristic zero.  2004 Published by Elsevier Inc.

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Abstract. Let Φ be an algebraically closed field of characteristic zero, G a finite, not necessarily abelian, group. Given a G-grading on the full matrix algebra A = M n (Φ), we decompose A as the tensor product of graded subalgebras A = B ⊗ C, B ∼ = M p (Φ) being a graded division algebra, while the grading of C ∼ = M q (Φ) is determined by that of the vector space Φ n . Now the grading of A is recovered from those of A and B using a canonical "induction" procedure.

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