Mathematics – Rings and Algebras
Scientific paper
2005-12-09
Mathematics
Rings and Algebras
Scientific paper
Let $R$ be a finite-dimensional algebra over an algebraically closed field $F$ graded by an arbitrary group $G$. We prove that $R$ is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite subgroup of $G$. If the characteristic of $F$ is zero or ${\rm char} F$ does not divide the order of any finite subgroup of $G$ then we prove that $R$ is graded simple if and only if it is a matrix algebra over a finite-dimensional graded division algebra.
Bahturin Y. A.
Sehgal S. K.
Zaicev M. V.
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