The lattice of ideals of a Lie algebra

  1. Pilar Benito Clavijo, M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Algebra

ISSN: 0021-8693

Año de publicación: 1995

Volumen: 171

Número: 2

Páginas: 347-369

Tipo: Artículo

DOI: 10.1006/JABR.1995.1015 SCOPUS: 2-s2.0-58149364815 WoS: WOS:A1995QF80000002 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Algebra

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

In this paper the Lie algebras in which the lattice formed by the ideals is complemented or complemented and distributive are classified. Moreover, it is shown that the derived algebra (arbitrary characteristic) and the solvable radical (characteristic zero) can be characterized in terms of the ideal lattice structure. The relationship between Lie algebras having isomorphic lattices of ideals is also studied. It turns out that, over algebraically closed fields of characteristic zero, the Frattini ideal is preserved under ideal lattice isomorphisms and, as a consequence of this fact, the nilpotent radical is preserved by this kind of isomorphism when the codimension of the derived algebra is at least two. © 1995 Academic Press. All rights reserved.