Anona, M.; Randriambololondrantomalala, P.; Ravelonirina, H. S. G. On the Lie algebras of polynomial vector fields. (Sur les algèbres de Lie des champs de vecteurs polynomiaux.) (French) Zbl 1250.17031 Afr. Diaspora J. Math. 10, No. 2, 87-95 (2010). 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. Cited in 3 Documents 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 Keywords:derivations; Lie algebra of polynomial vector fields; Euler’s field PDFBibTeX XMLCite \textit{M. Anona} et al., Afr. Diaspora J. Math. 10, No. 2, 87--95 (2010; Zbl 1250.17031) Full Text: Euclid