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...
On affine Kac-Moody Lie algebras
On commutation relations for 3-graded Lie algebras.
On geometry of curves of flags of constant type
We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope...
On Lie algebras in braided categories
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative...
On prime -graded Lie algebras of growth one.
On solvability of Lie rings with an automorphism of finite order.
On the adjoint map of homotopy abelian DG-Lie algebras
We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.
On the basic representation of the affine Kac-Moody Lie algebras
On the classification of 3-dimensional coloured Lie algebras
In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.
On the cohomology of nilpotent Lie algebras
On the combinatorics of Young-Capelli symmetrizers.
On the double Poincaré series of the enveloping algebras of certain graded Lie algebras.
On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.
On the uniqueness of the -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.
Operateurs differentiels de Shimura et espaces prehomogenes.