Quillen's lemma

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.

References

• Quillen, D. (1969). "On the endomorphism ring of a simple module over an enveloping algebra". Proceedings of the American Mathematical Society 21: 171–172. doi:10.1090/S0002-9939-1969-0238892-4.