A Lie algebra that can be written as a sum of two nilpotent subalgebras, is solvable

Details A Lie algebra that can be written as a sum of two nilpotent subalgebras, is solvable A Lie algebra that can be written as a sum of two nilpotent subalgebras, is solvable

2009-11-28

arxiv.org/abs/0911.5418v1

Math. Notes 50 (1991), 909-912

Mathematics

Rings and Algebras

AMS-LaTeX, 5 pages

Scientific paper

10.1007/BF01156132

This is an old paper put here for archeological purposes. It is proved that a finite-dimensional Lie algebra over a field of characteristic p>5, that can be written as a vector space (not necessarily direct) sum of two nilpotent subalgebras, is solvable. The same result (but covering also the cases of low characteristics) was established independently by V. Panyukov (Russ. Math. Surv. 45 (1990), No.4, 181-182), and the homological methods utilized in the proof were developed later in arXiv:math/0204004. Many inaccuracies in the English translation are corrected, otherwise the text is identical to the published version.

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