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

2001/02/02 by Rutwig Campoamor, Campoamor, Rutwig, José María Ancochea +2
Mathematics · #17B30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B30

paper · pdf · doi:10.48550/arxiv.math/0102014

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

openalex publication_date 2001/02/02 · arxiv created 2001/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \frakh such that the quotient \fracdim \frakh-dim Z(\frakh)dim Z(\frakh) is as small as wanted.

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