Cyclicity of some symmetric nilpotent centers

Algorithmic Derivation of Nilpotent Centers

To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and after for studying the bifurcation of limit cycles from it or from its period annulus. We give an effective algorithm in the search of necessary conditions for detecting nilpotent centers based in rece...

Counting Symmetric Nilpotent Matrices

We determine the number of nilpotent matrices of order n over Fq that are selfadjoint for a given nondegenerate symmetric bilinear form, and in particular find the number of symmetric nilpotent matrices.

Some properties of nilpotent Lie algebras

In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.

Some Amazing Properties of Spherical Nilpotent Orbits

Let G be a simple algebraic group defined over an algebraically closed field k of characteristic zero. Write g for its Lie algebra. Let x ∈ g be a nilpotent element and G·x ⊂ g the corresponding nilpotent orbit. The maximal number m such that (adx) 6= 0 is called the height of x or of G·x, denoted ht(x). Recall that an irreducible G-variety X is called G-spherical if a Borel subgroup of G has a...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups