Matrix representations for low dimensional Lie algebras.
Maximal solvable extensions of filiform algebras
It is already known that any filiform Lie algebra which possesses a codimension 2 solvable extension is naturally graded. Here we present an alternative derivation of this result.
Modules simples sur une algèbre de Lie nilpotente contenant un vecteur propre pour une sous-algèbre
Moduli of unipotent representations I: foundational topics
With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let be such a group. The stack of all representations of dimension is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack which is better behaved, and, in particular, admits a coarse algebraic space, which...
Multi-dimensional Cartan prolongation and special k-flags
Since the mid-nineties it has gradually become understood that the Cartan prolongation of rank 2 distributions is a key operation leading locally, when applied many times, to all so-called Goursat distributions. That is those, whose derived flag of consecutive Lie squares is a 1-flag (growing in ranks always by 1). We first observe that successive generalized Cartan prolongations (gCp) of rank k + 1 distributions lead locally to all special k-flags: rank k + 1 distributions D with the derived...