Narrow positively graded Lie algebras (Q1732074)

Let \(\mathfrak{g} = \displaystyle\bigoplus_{i=1}^{\infty} \mathfrak{g}_{i}\) be an infinite-dimensional, graded Lie algebra over the real or the complex numbers. In the main result of the paper under review, the author classifies the algebras \(\mathfrak{g}\) which satisfy \([\mathfrak{g}_{1}, \mathfrak{g}_{i}] = \mathfrak{g}_{i+1}\) for \(i \ge 1\), and the narrowness condition, in the sense of \textit{A. Shalev} and \textit{E. I. Zelmanov} [J. Math. Sci., New York 93, No. 6, 951--963 (1999; Zbl 0933.17011)], \[ \dim(\mathfrak{g}_{i}) + \dim(\mathfrak{g}_{i+1}) \le 3, \quad\text{ for }i \ge 1. \]