This work shows how to associate the Lie algebra hn, of upper triangular matrices, with a
specific combinatorial structure of dimension 2, for n∈ N. The properties of this structure are …

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals
of finite-dimensional Lie algebras, starting from the non-zero brackets in its law. In order to …

In this paper, the maximal abelian dimension is computationally obtained for an arbitrary
finite-dimensional Lie algebra, defined by its nonzero brackets. More concretely, we …

Abelian subalgebras play an important role in the study of Lie algebras and their properties
and structures. In this paper, the historical evolution of this concept is shown, analyzing the …

A finite dimensional Lie algebra L with magic number c (L) is said to satisfy Rentschler's
property if it admits an abelian Lie subalgebra H of dimension at least c (L)− 1. We study the …

The main goal of this paper is to compute the maximal abelian dimension of each solvable
nondecomposable Lie algebra of dimension less than 7. To do it, we apply an algorithmic …

The first part of this thesis focuses on the theme of group actions on smooth manifolds and
cohomology. Our contribution was to introduce a new cohomology attached to group actions …

The first part of this thesis focuses on the theme of group actions on smooth manifolds and
cohomology. Our contribution was to introduce a new differential subcomplex of the de …

This paper is devoted to the study of the maximal dimension of abelian Lie subalgebras of a
particular family of finite-dimensional Lie algebras: namely, Lie algebra) n, of n× n upper …

In this paper, the maximal abelian dimension is algorithmically and computationally studied
for the Lie algebra hn, of n× n upper-triangular matrices. More concretely, we define an …