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

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.

### MSC:

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