# Lie algebras of vector fields on smooth aﬃne varieties

@article{Billig2017LieAO, title={Lie algebras of vector fields on smooth aﬃne varieties}, author={Yuly Billig and Vyacheslav Futorny}, journal={Communications in Algebra}, year={2017}, volume={46}, pages={3413 - 3429} }

ABSTRACT We reprove the results of Jordan [18] and Siebert [30] and show that the Lie algebra of polynomial vector fields on an irreducible aﬃne variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth aﬃne variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N…

## 15 Citations

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