Related papers: A short note on 2-step nilpotent Lie algebras asso…

In this paper we study contact structure on 2-step nilpotent, Heisenberg type Lie groups. We decompose this Lie groups to center and orthogonal complement, then investigate properties of both orthogonal Lie subgroups. Finally, we provide a…

We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step…

In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated…

In this article we show that the only 2-step nilpotent Lie groups which carry a non-degenerate left invariant Killing-Yano 2-form are the complex Lie groups. In the case of 2-step nilpotent complex Lie groups arising from connected graphs,…

We propose the study and description of the structure of complex Lie algebras with nilradical a nilpotent Lie algebra of type 2 by using sl2(C)-representation theory. Our results will be applied to review the classification given in [1] (J.…

Any abstract (not necessarily continuous) group automorphism of a simple, compact Lie group must be continuous due to Cartan (1930) and van der Waerden (1933). The purpose of this paper is to study a similar question in nilpotent Lie…

We consider pairs (V,H) of subgroups of a connected unipotent complex Lie group G for which the induced VxH-action on G by multiplication from the left and from the right is free. We prove that this action is proper if the Lie algebra g of…

Motivated by the Dani-Mainkar construction, we extend the notion of independence polynomial of graphs to arbitrary 2-step nilpotent Lie algebras. After establishing efficiently computable upper and lower bounds for the independence number,…

We study symplectic (contact) structures on nilmanifolds that correspond to the filiform Lie algebras - nilpotent Lie algebras of the maximal length of the descending central sequence. We give a complete classification of filiform Lie…

In this work, we consider degenerations between 8-dimensional 2-step nilpotent Lie algebras over $\mathbb{C}$ and obtain the geometric classification of the variety $\mathcal{N}^2_8$.

We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure constants for these real Lie algebras.

The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…

First we describe the Skjelbred-Sund method for classifying nilpotent Lie algebras. Then we use it to classify 6-dimensional nilpotent Lie algebras over any field of characteristic not 2. The proof of this classification is essentially…

Let $L$ be a finite-dimensional Lie algebra over a field $F$. In This paper we introduce the \emph{nilpotent graph} $\Gamma_\mathfrak{N}(L)$ as the graph whose vertices are the elements of $L \setminus \nil(L)$, where \[\nil(L) = \{x \in L…

By using the concept of weight graph associated to certain nilpotent Lie algebras $\frak{g}$, we find necessary and sufficient conditions for a semidirect product $\frak{g}\oplus T_{i}$, where $T_{i}<T$ is a subalgebra of a maximal torus of…

We introduce and investigate the solvable graph $\Gamma_\mathfrak{S}(L)$ of a finite-dimensional Lie algebra $L$ over a field $F$. The vertices are the elements outside the solvabilizer $\sol(L)$, and two vertices are adjacent whenever they…

We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is…

We associate a graph ${\mathcal N}_{S}$ with a semigroup $S$ (called the upper non-nilpotent graph of $S$). The vertices of this graph are the elements of $S$ and two vertices are adjacent if they generate a semigroup that is not nilpotent…

In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they…

In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real…