Classification of graded Lie algebras with two generators. (English. Russian original) Zbl 0533.17008

Fialowski, A.

Mosc. Univ. Math. Bull. 38, No. 2, 76-79 (1983); translation from Vestn. Mosk. Univ., Ser. I 1983, No. 2, 62-64 (1983).

This article classifies infinite-dimensional Lie algebras over a field of characteristic zero with basis \(e_ 1,e_ 2,e_ 3,\dots\) satisfying \([e_ i,e_ j]=c_{ij}e_{i+j}\) and having two generators. From this classification it follows that if the number of independent relations between the generators of such an algebra is finite, then it is equal to two.

Reviewer: Gordon Brown (Boulder)

MSC:

17B65	Infinite-dimensional Lie (super)algebras
17B70	Graded Lie (super)algebras

Keywords:

infinite-dimensional Lie algebras; characteristic zero; two generators