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On the Lie algebras of polynomial vector fields. (Sur les algèbres de Lie des champs de vecteurs polynomiaux.) (French) Zbl 1250.17031

Summary: We study the derivation of the Lie algebra of polynomial vector fields over \(\mathbb R^n\) which contain all the constant fields and Euler’s field. It is adjoint to the normalizer of the Lie algebra of polynomial vector fields over \(\mathbb R^n\). If, moreover, the Lie algebra contains all diagonal linear fields, then all its derivations are inner. We give a classification of this Lie algebra.

MSC:

17B66 Lie algebras of vector fields and related (super) algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
17B56 Cohomology of Lie (super)algebras
17B70 Graded Lie (super)algebras
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Full Text: Euclid