On k-abelian, p-filiform Lie algebras

2000/07/28 by Otto Rutwig Campoamor, Campoamor, Otto Rutwig
Biochemistry, Genetics and Molecular Biology · Mathematics · #17B30 #17B56 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Sphingolipid Metabolism and Signaling #math.RA #msc:17B30 #msc:17B56

paper · pdf · doi:10.48550/arxiv.math/0007176

22 Latex Pages. Part of the communication given in the I Colloquium of Lie theory celebrated in Vigo 17-22 july 2000

openalex publication_date 2000/07/28 · arxiv created 2001/08/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the (n-5)-filiform Lie algebras which have the additional property of a non-abelian derived subalgebra. We show that this property is strongly related with the structure of the Lie algebra of derivations; explicitely we show that if a (n-5)-filiform algebra is characteristically nilpotent, then it must be 2-abelian. We also give applications of k-abelian Lie algebras to the construction of solvable rigis algebras, as well as to the theory of nilalgebras of parabolic subalgebras in the example of the exceptional simple model E₆.

Related

• Classification of (n-5)-filiform Lie algebras
• Nonfiliform characteristically nilpotent Lie algebras
• Non-singular derivations of solvable Lie algebras in prime characteristic
• Almost inner derivations of Lie algebras II
• Sur les algèbres de Lie quasi-filiformes admettant un tore de dérivations [On quasi-filiform Lie algebras admitting a torus of derivations]