Geodesic
Non-splittable extensions of a general Lie algebra of Cartan type $W_2(\overline m)$
Sbornik. Mathematics, Tome 186 (1995) no. 4, pp. 527-554

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In this paper we compute the extensions of a general Lie algebra of Cartan type in two variables $W_2(\overline m)$ by irreducible modules. Part of the results covers a still more general case. 
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     title = {Non-splittable extensions of a general {Lie} algebra of {Cartan} type $W_2(\overline m)$},
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A. S. Dzhumadil'daev; U. U. Umirbaev. Non-splittable extensions of a general Lie algebra of Cartan type $W_2(\overline m)$. Sbornik. Mathematics, Tome 186 (1995) no. 4, pp. 527-554. http://geodesic.mathdoc.fr/item/SM_1995_186_4_a3/