Zur Konstruktion nilpotenter Lie-Algebren. (On the construction of nilpotent Lie algebras). (German) Zbl 0706.17004
Wiss. Z., Pädagog. Hochsch. “Liselotte Herrmann” Güstrow, Math.- Naturwiss. Fak. 27, No. 2, 237-246 (1989).
The author aims at upper and lower bounds for the number of defining relations belonging to \(L^ m(X)\), the vector spaces with homogeneous summand of the free Lie algebra L(X) of degree d. She obtains the following inequality
\[
\frac{(m-1)^{m-1}}{m^ m}\leq \limsup_{d\to \infty}\frac{r}{d^ m}\leq \frac{2^{m-1}-1}{2^{m-1}\cdot m}
\]
and gives an example with small system of relations.
Reviewer: H.Heineken