On the product by generators of characteristically nilpotent Lie S-algebras

Abstract

We introduce the product by generators of complex nilpotent Lie algebras, which is a commutative product obtained from a central extension of the direct sum of Lie algebras. We show that the product preserves also the characteristic nilpotence provided that the multiplied algebras are $S$-algebras. In particular, this shows the existence of nonsplit characteristically nilpotent Lie algebras $\mathfrak{h}$ such that the quotient $\frac{\dim \mathfrak{h}-\dim Z(\mathfrak{h})}{\dim Z(\mathfrak{h})}$ is as small as wanted.

8 Latex pages Mistake in the proof of prop. 1 deleted