Finite-dimensional simple graded algebras

Let $R$ be a finite-dimensional algebra over an algebraically closed field $F$ graded by an arbitrary group $G$. In the paper it is proved that if the characteristic of $F$ is zero or does not divide the order of any finite subgroup of $G$, then $R$ is graded simple if and only if it is isomorphic to a matrix algebra over a finite-dimensional graded skew field.
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