Sage computations of sl2(k)-Levi extensions
ISSN: 1512-0139
Datum der Publikation: 2012
Ausgabe: 5
Nummer: 2
Seiten: 3-17
Art: Artikel
Andere Publikationen in: Tbilisi Mathematical Journal
Projekte im Zusammenhang
Zusammenfassung
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.