La structure de Poisson sur l'algèbre symétrique d'une algèbre de Lie nilpotente
Las álgebras de Lie (n-3)-filiformes como extensiones por derivaciones.
Left-symmetric algebras, or pre-Lie algebras in geometry and physics
In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs...
Leibniz -algebras
A finite-dimensional Lie algebra is called an -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.
Les modules simples sphériques d'une algèbre de Lie nilpotente
Lie algebras all of whose subalgebras are supersolvable.
A Lie algebra L is said to be minimal non supersolvable if all its subalgebras, except L itself, are supersolvable.
Lie algebras of least cohomology.
Lie groups with no left invariant complex structures
Lie solvable groups algebras of derived length three.
Let K be a field of characteristic p > 2 and let G be a group. Necessary and sufficient conditions are obtained so that the group algebra KG is strongly Lie solvable of derived length at most 3. It is also shown that these conditions are equivalent to KG Lie solvable of derived length 3 in characteristic p ≥ 7.
Lie-Algebren mit Idealisatorbedingung
Lie-Algebren mit SI-Bedingungen.
Linear equations in nilpotent Lie rings. (Equations linéaires dans les anneaux nilpotents au sens de Lie.)
L'injectivité de l'application de Dixmier pour les algèbres de Lie résolubles.
Locally coalescent classes of Lie algebras
Low-dimensional filiform Lie superalgebras.
The aim of this paper is to give a classification up to isomorphism of low dimension filiform Lie superalgebras.