Abstract
We prove that an infinite-dimensional Lie algebra over an arbitrary field which is decomposable into the sum of two of its subalgebras with finite-dimensional commutants is almost solvable.
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References
N. Itô, “Ueber das Produkt von zwei abelschen Gruppen,”Math. Z.,62, No. 4, 400–401 (1955).
A. I. Kostrikin, “A criterion of solvability of a finite-dimensional Lie algebra,”Vestn. Mosk. Univ. Mat., Mekh., No. 2, 5–8 (1982).
D. I. Zaitsev, “Itô theorem and group products,”Mat. Zametki,33, No. 6, 807–818 (1983).
N. S. Chernikov, “Factorization of groups by almost BFC-groups,” in:Infinite Groups and Related Algebraic Structures [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993), pp. 367–387.
V. V. Panyukov, “On solvability of a finite-dimensional Lie algebra of positive characteristic,”Usp. Mat. Nauk,45, No. 4, 163–164 (1990).
O. H. Kegel, “Zur Nilpotenz gewisser assoziativer Ringe,”Math. Ann.,149, No. 3, 258–260 (1963).
A. P. Petravchuk, “Lie algebras decomposable into the sum of an Abelian subalgebra and a nilpotent subalgebra,”Ukr. Mat. Zh.,40, No. 3, 385–388 (1988).
I. Stewart, “Lie algebras generated by finite-dimensional ideals,”Res. Notes., Math.,2 (1972).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 8, pp. 1089–1096, August, 1995.
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Petravchuk, A.P. On the sum of two Lie algebras with finite-dimensional commutants. Ukr Math J 47, 1244–1252 (1995). https://doi.org/10.1007/BF01057713
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DOI: https://doi.org/10.1007/BF01057713