The occurrence problem for Lie algebras
The author proves undecidability of the occurrence problem for: 1) finitely generated right ideals in the universal enveloping algebra of a free metabelian Lie algebra of a large enough rank (Theorem 1); 2) finitely generated subalgebras of a free solvable Lie algebra of solvability index \(\geq 3\) and of a large enough rank (Theorem 2); 3) finitely generated subalgebras of the free product \(L*L_ 1\) where \(L\) is a free metabelian Lie algebra of a large enough rank and \(L_ 1\) is a one-dimensional Lie algebra (Theorem 3). Theorem 3 gives the negative answer to G. Kukin's problem 1.86 in [Dnestr. Notebook, Novosibirsk (1982; Zbl 0493.16001)].
scientific article; zbMATH DE number 738952