Geodesic
Group Gradings on Matrix Algebras
Canadian mathematical bulletin, Tome 45 (2002) no. 4, pp. 499-508

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DOI

Let $\Phi $ be an algebraically closed field of characteristic zero, $G$ a finite, not necessarily abelian, group. Given a $G$ -grading on the full matrix algebra $A\,=\,{{M}_{n}}\left( \Phi\right)$ , we decompose $A$ as the tensor product of graded subalgebras $A\,=\,B\,\otimes \,C,\,B\,\cong \,{{M}_{p}}\left( \Phi\right)$ being a graded division algebra, while the grading of $C\,\cong \,{{M}_{q}}\left( \Phi\right)$ is determined by that of the vector space ${{\Phi }^{n}}$ . Now the grading of $A$ is recovered from those of $A$ and $B$ using a canonical “induction” procedure.
DOI : 10.4153/CMB-2002-051-x
Mots-clés : 16W50 
Bahturin, Yu. A.; Zaicev, M. V. Group Gradings on Matrix Algebras. Canadian mathematical bulletin, Tome 45 (2002) no. 4, pp. 499-508. doi: 10.4153/CMB-2002-051-x
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     title = {Group {Gradings} on {Matrix} {Algebras}},
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