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Lie algebras of vector fields on smooth affine varieties. (arXiv:1705.05900v1 [math.RT])
来源于:arXiv
We 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. This completes
the result of Jordan on the simplicity of the derivation algebra \cite{Jo}.
Given proof is self-contained and does not depend on the results of Jordan.
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-dimensional
sphere, non-singular hyperelliptic curves and linear algebraic groups are
considered. 查看全文>>