Local universal algebras and reduced representations of Lie algebras

We consider representations of Lie algebras over a field of characteristic $p>0$. We introduce local universal algebras, and we show that the study of the reduced representations of a Lie algebra reduces to the study of the representations of the local universal algebra of the Lie algebra. In certain cases, this enables us to reduce the study of the reduced representations of a Lie algebra to the study of the representations of a commutative ring.
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