Algorithmic problems for solvable Lie algebras
It is proved that any variety \(\mathfrak M\) of Lie algebras which contains the variety \(\mathfrak N_2\mathfrak A\), has the unsolvable word problem. This result is more general than the theorem of the reviewer about unsolvability of the word problem for the class of all Lie algebras [see Izv. Akad. Nauk SSSR, Ser. Mat. 36, 1173--1219 (1972; Zbl 0252.02046)] and gives the positive answer to the well-known problem of \textit{A. I. Shirshov} [see Dnestr Notebook, Novosibirsk, 1976, problem No. 155] about unsolvability of the word problem for the \(n\)-solvable Lie algebra, \(n\ge 3\).
scientific article; zbMATH DE number 3695427