On Levi extensions of nilpotent Lie algebras

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

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Linear Algebra and Its Applications

ISSN: 0024-3795

Year of publication: 2013

Volume: 439

Issue: 5

Pages: 1441-1457

Type: Article

Export: RIS
DOI: 10.1016/j.laa.2013.04.027 SCOPUS: 2-s2.0-84879230992 WoS: 000321320700017 arXiv: 1302.4255v1 GOOGLE SCHOLAR lock_openOpen access editor
Institutional repository: lock_openOpen access editor


Cited by

  • Scopus Cited by: 2 (14-07-2021)

Journal Citation Reports

  • Year 2013
  • Journal Impact Factor: 0.983
  • Best Quartile: Q2
  • Area: MATHEMATICS, APPLIED Quartile: Q2 Rank in area: 84/251 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2013
  • SJR Journal Impact: 0.985
  • Best Quartile: Q1
  • Area: Algebra and Number Theory Quartile: Q1 Rank in area: 19/91
  • Area: Discrete Mathematics and Combinatorics Quartile: Q1 Rank in area: 10/62
  • Area: Geometry and Topology Quartile: Q2 Rank in area: 22/86
  • Area: Numerical Analysis Quartile: Q2 Rank in area: 15/66


  • Year 2013
  • CiteScore of the Journal : 1.8
  • Area: Algebra and Number Theory Percentile: 90
  • Area: Discrete Mathematics and Combinatorics Percentile: 85
  • Area: Geometry and Topology Percentile: 76
  • Area: Numerical Analysis Percentile: 54


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.