# Quillen's lemma

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In algebra, **Quillen's lemma** states that an endomorphism of a simple module over the enveloping algebra of a finite-dimensional Lie algebra over a field *k* is algebraic over *k*. In contrast to a version of Schur's lemma due to Dixmier, it does not require *k* to be uncountable. Quillen's original short proof uses generic flatness.