On Levi extensions of nilpotent Lie algebras

  1. Benito, P. 1
  2. De-La-Concepción, D. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Linear Algebra and Its Applications

ISSN: 0024-3795

Ano de publicación: 2013

Volume: 439

Número: 5

Páxinas: 1441-1457

Tipo: Artigo

DOI: 10.1016/J.LAA.2013.04.027 SCOPUS: 2-s2.0-84879230992 WoS: WOS:000321320700017 arXiv: 1302.4255v1 GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: Linear Algebra and Its Applications

Repositorio institucional: lock_openAcceso aberto Editor

Proxectos relacionados

Álgebras, triples y lazos relacionados con Geometría y Supermetría

2011/00007/001

Resumo

Levi's theorem decomposes any arbitrary Lie algebra over a field of characteristic zero, as a direct sum of a semisimple Lie algebra (named Levi factor) and its solvable radical. Given a solvable Lie algebra R, a semisimple Lie algebra S is said to be a Levi extension of R in case a Lie structure can be defined on the vector space S ⊕ R. The assertion is equivalent to ρ (S) ⊆ Der (R), where Der(R) is the derivation algebra of R, for some representation ρ of S onto R. Our goal in this paper, is to present some general structure results on nilpotent Lie algebras admitting Levi extensions based on free nilpotent Lie algebras and modules of semisimple Lie algebras. In low nilpotent index a complete classification will be given. The results are based on linear algebra methods and leads to computational algorithms. © 2013 Elsevier Inc. All rights reserved.