Graded Lie algebras of maximal class IV
Graded Lie algebras with classical reductive null component.
Graded Lie algebras with few nontrivial components.
Graded Lie algebras with finite polydepth
Graded nilpotent Lie algebra of rank 3 and inverse of a differential operator. (Algèbre de Lie nilpotente graduée de rang 3 et inverse d'un opérateur différentiel.)
Graded nilpotent Lie algebras in low dimensions.
Graded subalgebras of the Lie algebra of a smooth manifold.
Growth and Lie brackets in the homotopy Lie algebra.
Homology and modular classes of Lie algebroids
For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.
La décomposition en poids des algèbres de Hopf
Si est une algèbre de Hopf commutative ou cocommutative et connexe, les puissances de convolution et le logarithme, au sens du produit de convolution, du morphisme identité de satisfont à diverses identités algébriques. L’algèbre de Hopf admet en particulier une décomposition en poids sous l’action des morphismes , dont nous étudions les propriétés.
Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy.
Lie algebras graded by the root system .
Lie superalgebras graded by the root system .
Low-dimensional filiform Lie superalgebras.
The aim of this paper is to give a classification up to isomorphism of low dimension filiform Lie superalgebras.
Modular vector fields and Batalin-Vilkovisky algebras
We show that a modular class arises from the existence of two generating operators for a Batalin-Vilkovisky algebra. In particular, for every triangular Lie bialgebroid (A,P) such that its top exterior power is a trivial line bundle, there is a section of the vector bundle A whose -cohomology class is well-defined. We give simple proofs of its properties. The modular class of an orientable Poisson manifold is an example. We analyse the relationships between generating operators of the Gerstenhaber...
Monstrous moonshine and monstrous Lie superalgebras.
-wave equations with orthogonal algebras: and reductions and soliton solutions.
Normal Lie subsupergroups and non-abelian supercircles.
On 3-graded Lie algebras, Jordan pairs and the canonical kernel function.
On a nilpotent Lie superalgebra which generalizes Qn.
In Gilg (2000, 2001) the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra Ln are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Qn, which only exists in even dimension as a consequence of the centralizer property. Certain...