zbMATH — the first resource for mathematics

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].

17B01 Identities, free Lie (super)algebras
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.