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Finitely generated subalgebras of a free product of Lie algebras. (English. Russian original) Zbl 0588.17016

Sov. Math. 28, No. 4, 40-46 (1984); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1984, No. 4(263), 32-37 (1984).
The author follows G. P. Kukin’s techniques to obtain the following result. Let S be a subalgebra of the free product A*B of Lie algebras A and B. If S is finitely generated and its intersections \(S\cap A\) and \(S\cap B\) are finitely presented then S is finitely presented. There are also two results in the paper that give a version of Kurosh’s Subgroup Theorem (known to be false in the setting of Lie algebras) for residually finite Lie algebras.
Reviewer: Yu.A.Bakhturin

MSC:

17B99 Lie algebras and Lie superalgebras
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