Relaciones entre la estructura de un álgebra de Lie y el retículo de sus ideales

Abstract

The lattice of ideals of a Lie algebra is closely related with the structure of the algebra. In the first chapter, some classes of Lie algebras are selected. It is studied if their lattices of ideals can determinate their algebraic structures. In the second chapter, two classes of lattices are studied: the complemented lattices and the lattices such their elements are in line. We characterize the Lie algebras of complemented lattice of ideals. As a consequence, it is obtained the reticular determination of the reductive Lie algebras. Finally, we characterize the supersolvable Lie algebras whose ideals are in line.