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Group Gradings on Matrix Algebras

Open Access article
 Printed: Dec 2002
  • Yu. A. Bahturin
  • M. V. Zaicev
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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 $A = M_n(\Phi)$, we decompose $A$ as the tensor product of graded subalgebras $A = B\otimes C$, $B\cong M_p (\Phi)$ being a graded division algebra, while the grading of $C\cong M_q (\Phi)$ 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.
MSC Classifications: 16W50 show english descriptions Graded rings and modules 16W50 - Graded rings and modules

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