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Finite dimensional graded simple algebras

Y. A. Bahturin·S. K. Sehgal·M. V. Zaicev
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Abstract

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.

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Y. A. Bahturin, S. K. Sehgal, M. V. Zaicev. 2005-12-09. Finite dimensional graded simple algebras. https://arxiv.org/abs/math/0512202

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