On solvable Lie algebras decomposable into a~sum of two nilpotent subalgebras
Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 221-235

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Finite-dimensional Lie algebras over an algebraically closed field of positive characteristic representable as a sum (not necessarily direct) of two nilpotent subalgebras are studied. Necessary and sufficient conditions are obtained for a Lie algebra to be decomposable into a sum of two Cartan subalgebras.
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V. V. Panyukov. On solvable Lie algebras decomposable into a~sum of two nilpotent subalgebras. Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 221-235. http://geodesic.mathdoc.fr/item/SM_1995_83_1_a10/