On extensions of free nilpotent Lie algebras of type 2

  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

Año de publicación: 2014

Volumen: 457

Páginas: 363-382

Tipo: Artículo

DOI: 10.1016/J.LAA.2014.05.039 SCOPUS: 2-s2.0-84902314021 WoS: WOS:000340330700023 GOOGLE SCHOLAR

Otras publicaciones en: Linear Algebra and Its Applications

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

In this paper, we study the structure of Lie algebras which have free t-nilpotent Lie algebras n2,t of type 2 as nilradical and give a detailed construction for them. We prove that the dimension of any Lie algebra g of this class is dimn2,t+k. If g is solvable, k≤2 otherwise, the Levi subalgebra of g is sl2(K), the split simple 3-dimensional Lie algebra of 2;times&2 matrices of trace zero, and then k≤4. As an application of the main results we get the classification over algebraically closed fields of Lie algebras with nilradical n2,1, n2,2 and n2,3. © 2014 Published by Elsevier Inc.