We give a construction of nonsmooth self-dual projective algebraic varieties. They appear as certain projectivized orbit closures for some linear actions of reductive algebraic groups. Applying this construction to adjoint representations, we obtain geometric characterization of distinguished nilpotent elements of semisimple Lie algebras [BC1], [BC2] (i.e., nilpotent elements whose centralizer ...

According to a folklore result, every regular map on an orientable surface with abelian automorphism group belongs to one of three infinite families of maps with one or two vertices. Here we deal with regular maps whose automorphism group is nilpotent. We show that each such map decomposes into a direct product of two maps H×K, where Aut(H) is a 2-group and K is a map with a single vertex and a...

We study the existence of Fuchsian differential equations in positive characteristic with nilpotent p-curvature, and given local invariants. In the case of differential equations with logarithmic local mononodromy, we determine the minimal possible degree of a polynomial solution. 2000 Mathematical Subject Classification: Primary 14D10, 12H20 This paper deals with second order differential equa...

We show that if K is a nilpotent finite complex, then ΩK can be built from spheres using fibrations and homotopy (inverse) limits. This is applied to show that if map∗(X,S ) is weakly contractible for all n, then map ∗ (X,K) is weakly contractible for any nilpotent finite complex K . AMS Classification numbers Primary: 55Q05 Secondary: 55P50

Dyer and Formanek (1976) proved that if N is a free nilpotent group of class two and of rank 6= 1, 3, then the automorphism group Aut(N) of N is complete. The main result of this paper states that the automorphism group of an infinitely generated free nilpotent group of class two is also complete.

Gromov conjectured that the fundamental group of a manifold with almost nonnegative Ricci curvature is almost nilpotent. This conjecture is proved under the additional assumption on the conjugate radius. We show that there exists a nilpotent subgroup of finite index depending on a lower bound of the conjugate radius.

Hedlund [He] constructed Riemannian metrics on n-tori, n ≥ 3 for which minimal geodesics are very rare. In this paper we construct similar examples for every nilpotent fundamental group. These examples show that Bangert’s existence results of minimal geodesics [Ba2] are optimal for nilpotent fundamental groups.

We prove that if L = lim ←−Ln (n ∈ N), where each Ln is a finite dimensional semisimple Lie algebra, and A is a finite codimensional ideal of L, then L/A is also semisimple. We show also that every finite dimensional homomorphic image of the cartesian product of solvable (nilpotent) finite dimensional Lie algebras is solvable (nilpotent). Mathematics Subject Classification: 14L, 16W, 17B45

We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra g and the orbits of Q̌/(h + 1)Q̌ under the Weyl group (Q̌ being the coroot lattice and h the Coxeter number of g). From this result we deduce in a uniform way a counting formula for the ad-nilpotent ideals.

The aim of this work is to present the first problems that appear in the study of nilpotent Leibniz superalgebras. These superalgebras and so the problems, will be considered as a natural generalization of nilpotent Leibniz algebras and Lie superalgebras. 2000 MSC: 17A32, 17B30. Key-Words: Lie superalgebras, Leibniz superalgebras, nilindex.