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Bases of a free Lie algebra. (English. Russian original) Zbl 0404.17013
Math. Notes 24, 700-704 (1979); translation from Mat. Zametki 24, 375-382 (1978).
Summary: In this paper a method is proposed for choosing a basis for a free Lie algebra. This method is more general than the one of A. I. Shirshov [Algebra Logika 1, No. 1, 14–19 (1962; Zbl 0145.25803)]. Examples are given involving a choice of basis of a free Lie algebra. A basis of a free Lie algebra is exhibited which consists of right-normalized monomials.
These results were announced previously in [Third All-Union Symposium on Ring Theory, Modules, and Algebras (in Russian), Tartu (1976), pp. 62–63].

MSC:
17B01 Identities, free Lie (super)algebras
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References:
[1] A. I. Shirshov, ?On bases of a free algebra,? Algebra Logika,1, No. 1, 14-19 (1962). · Zbl 0145.25803
[2] G. P. Kukin, ?A method for choosing a basis of a free Lie algebra,? in: Third All-Union Symposium on Ring Theory, Modules, and Algebras [in Russian], Tartu (1976), pp. 62-63.
[3] A. I. Shirshov ?Subalgebras of free Lie algebras,? Mat. Sb.,33, No. 2, 441-452 (1953). · Zbl 0052.03004
[4] G. P. Kukin, ?On the equality problem for Lie algebras,? Sib. Mat. Zh.,18, No. 5, 1192-1195 (1977).
[5] N. Bourbaki, Groupes et Algèbres de Lie, Paris. · Zbl 0199.35203
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