We associate to each nilpotent orbit of a real semisimple Lie algebra go a weighted Vogan diagram, that is a Dynkin diagram with an involution of the diagram, a subset of painted nodes and a weight for each node. Every nilpotent element of go is noticed in some subalgebra of go. In this paper we characterize the weighted Vogan diagrams associated to orbits of noticed nilpotent elements.

Let G be an arbitrary group. We show that if the Fitting subgroup of G is nilpotent then it is definable. We show also that the class of groups whose Fitting subgroup is nilpotent of class at most n is elementary. We give an example of a group (arbitrary saturated) whose Fitting subgroup is definable but not nilpotent. Similar results for the soluble radical are given.

We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse semigroup, the symmetric semigroup, and the factor power of the symmetric group. We also apply this approach to obtain a classification of maximal nilpotent...

This paper presents a novel approach to continuously and robustly tracking critical (geometrically, perpendicular and/or extremal) distances from a moving plane point p ∈ R to a static parametrized piecewise rational curve γ(s) (s ∈ R). The approach is a combination of local marching, and the detection and computation of global topological change, both based on the differential properties of a ...

— Let g be a finite dimensional complex reductive Lie algebra and S(g) its symmetric algebra. The nilpotent bicone of g is the subset of elements (x, y) of g×g whose subspace generated by x and y is contained in the nilpotent cone. The nilpotent bicone is naturally endowed with a scheme structure, as nullvariety of the augmentation ideal of the subalgebra of S(g) ⊗C S(g) generated by the 2-orde...

I show that simple finite vertex algebras are commutative, and that the Lie conformal algebra structure underlying a reduced (= without nilpotent elements) finite vertex algebra is nilpotent.

We construct examples of two-step and three-step nilpotent Lie groups whose automorphism groups are “small” in the sense of either not having a dense orbit for the action on the Lie group, or being nilpotent (the latter being stronger). From the results we also get new examples of compact manifolds covered by two-step simply connected nilpotent Lie groups which do not admit Anosov automorphisms...

In this paper, the existence, multiplicity and noexistence of positive solutions for a class of semipositone discrete boundary value problems with two parameters is studied by applying nonsmooth critical point theory and sub-super solutions method. Keywords—Discrete boundary value problems, nonsmooth critical point theory, positive solutions, semipositone, sub-super solutions method

We consider N = 2 super Yang-Mills theory with SU(2) gauge group and a single quark hypermultiplet in the fundamental representation. For a specific value of the quark bare mass and at a certain point in the moduli space of vacua, the central charges corresponding to two mutually non-local electro-magnetic charges vanish simultaneously, indicating the possibility of massless such states in the ...