Quelques bases et familles basiques des algèbres de Lie libres commodes pour les calculs sur ordinateurs
Représentations indécomposables de dimension finie des algèbres de Lie.
Rings with involution whose symmetric elements are central.
SCAP-subalgebras of Lie algebras
A subalgebra of a finite dimensional Lie algebra is said to be a -subalgebra if there is a chief series of such that for every , we have or . This is analogous to the concept of -subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its -subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.
Sobre derivaciones de algebras de Lie
Sobre derivaciones exteriores de algebras de Lie
Soluble subideals of Lie algebras
Solvable extensions of a special class of nilpotent Lie algebras
A pair of sequences of nilpotent Lie algebras denoted by and are introduced. Here denotes the dimension of the algebras that are defined for ; the first term in the sequences are denoted by 6.11 and 6.19, respectively, in the standard list of six-dimensional Lie algebras. For each of and all possible solvable extensions are constructed so that and serve as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program of investigating...
Some properties of generalized reduced Verma modules over -graded modular Lie superalgebras
We study some properties of generalized reduced Verma modules over -graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for -graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules.
Structure of perfect Lie algebras without center and outer derivations
Sur certaines classes d'algèbres de Lie rigides.
Sur la structure des algèbres de Lie rigides
On étudie la structure des algèbres de Lie rigides sur un corps algébriquement clos de caractéristique 0. Elles sont algébriques. Quand le radical est non nilpotent leur dimension est la même que celle de l’algèbre des dérivations. Quand le radical est nilpotent elle appartient à l’un des cas suivants : parfaite, produit direct d’une algèbre parfaite par le corps de base ou encore toutes les dérivations semi-simples sont intérieures.
Sur les crochets généralisés et quelques unes de leurs applications
Sur les orbites de la représentation coadjointe
Sur l'indice de certaines algèbres de Lie
On donne une majoration de l'indice de certaines algèbres de Lie introduites par V. Dergachev, A. Kirillov et D. Panyushev. On en déduit la preuve d'une conjecture de D. Panyushev. Nous formulons aussi une conjecture concernant l'indice de ces algèbres, et la prouvons dans des cas particuliers. Enfin, nous donnons un résultat concernant l'indice des sous-algèbres paraboliques d'une algèbre de Lie semi-simple.
Sur une famille d'algèbres de Lie idéalement finies
Symmetry algebras and normal forms of third order ordinary differential equations.
The approximative centre of a Lie algebra.
The classification of Lie algebras with invariant cones.
The classification of two step nilpotent complex Lie algebras of dimension
A Lie algebra is called two step nilpotent if is not abelian and lies in the center of . Two step nilpotent Lie algebras are useful in the study of some geometric problems, such as commutative Riemannian manifolds, weakly symmetric Riemannian manifolds, homogeneous Einstein manifolds, etc. Moreover, the classification of two-step nilpotent Lie algebras has been an important problem in Lie theory. In this paper, we study two step nilpotent indecomposable Lie algebras of dimension over the...