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

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

2001-02-02

arxiv.org/abs/math/0102014v2

Mathematics

Rings and Algebras

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

Scientific paper

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 $\frak{h}$ such that the quotient $\frac{\dim \frak{h}-\dim Z(\frak{h})}{\dim Z(\frak{h})} $ is as small as wanted.

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