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

الأصل · EN

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 h such that the quotient h- Z(h) Z(h) is as small as wanted.