Geodesic
Deformations of the Lie algebras $W_n(\mathbf m)$
Sbornik. Mathematics, Tome 66 (1990) no. 1, pp. 169-187 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the Gerstenhaber deformations of a general Lie algebra of Cartan type $W_n(\mathbf m)$ are computed. In particular, it is shown that $W_n(\mathbf m)$ is rigid over a perfect field. The Albert–Frank algebra is generalized to the case of several variables, and a criterion for such an algebra to be simple is obtained. Bibliography: 13 titles. 
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A. S. Dzhumadil'daev. Deformations of the Lie algebras $W_n(\mathbf m)$. Sbornik. Mathematics, Tome 66 (1990) no. 1, pp. 169-187. http://geodesic.mathdoc.fr/item/SM_1990_66_1_a8/

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