Sage computations of sl2(k)-Levi extensions

  1. Benito Clavijo, María del Pilar
  2. Concepción Sáez, Daniel de la
Tbilisi Mathematical Journal

ISSN: 1512-0139

Year of publication: 2012

Volume: 5

Issue: 2

Pages: 3-17

Type: Article

More publications in: Tbilisi Mathematical Journal


In 2010, Snolb [9] studied the structure of nilpotent Lie algebras admitting a Levi extension. As a corollary of the results therein, it is shown that the classes of characteristically nilpotent or filiform Lie algebras do not admit Levi extensions. The paper ends by asking for the possibility of finding series of nilpotent Lie algebras in arbitrary dimension not being abelian or Heisenberg and allowing such extensions. Our goal in this work is to present computational examples of this type of algebras by using Sage software. In the case of nilpotent Lie algebras admitting sl2(k) as Levi factor special constructions will be given by means of Sage routines based on transvections over sl2(k)-irreducible modules.