Deformations of the Lie algebras $W_n(\mathbf m)$

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.