In a recent article [Gi99], V.Ginzburg introduced and studied in depth the notion of a principal nilpotent pair in a semisimple Lie algebra g. He also obtained several results for more general pairs. As a next step, we considered in [Pa99] almost principal nilpotent pairs. The aim of this paper is to make a contribution to the general theory of nilpotent pairs. Roughly speaking, a nilpotent pai...

The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves to direct count of the isomorphism classes (notably in the case of nilpotent loops of order 2q, q a prime), or lead to efficient classification computer programs. This allows us to enumerate all nilpotent loops of orde...

To each complex semisimple Lie algebra $$ \mathfrak{g} and regular element a ∈ reg, one associates Mishchenko–Fomenko subalgebra \mathcal{F} ⊆ ℂ[ ]. This amounts to completely integrable system on the Poisson variety , as such has bifurcation diagram Σa Spec( a). We prove that codimension in a) if reg is not nilpotent, it or two nilpotent. In nilpotent case, we show of possible codimensions be ...

In the paper we describe class of all solvable extensions an infinite-dimensional filiform Leibniz algebra. The algebra is taken as a maximal pro-nilpotent ideal residually It proven that second cohomology group extension trivial.

We show that the right ideal of a Novikov algebra generated by square nilpotent subalgebra is nilpotent. also prove [Formula: see text]-graded text] over field with solvable text]-component solvable, where finite additive abelean group and characteristic does not divide order text]. any automorphisms if invariants solvable.

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over F(2(n)). Let G be an adjoint algebraic group of type B, C, or D defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the Lie algebra of G.

We consider the shape of balls for nilpotent Lie groups endowed with a left invariant Riemannian or sub-Riemannian metric. We prove that when the algebra is graded these balls are homeomorphic to the standard Euclidean ball. For two-step nilpotent groups we show that the intersections of the ball with the central cosets are star-shaped, and in special cases convex.

In this paper we investigate extensions of Gödel and Nilpotent Minimum logics by adding rational truth-values as truth constants in the language and by adding corresponding book-keeping axioms for the truth-constants. We also investigate the rational extensions of some parametric families of Weak Nilpotent Minimum logics, weaker than both Gödel and Nilpotent Minimum logics. Weak and strong stan...

We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.