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A constructive method to determine the variety of filiform Lie algebras

F. J. Echarte, M. C. Márquez, J. Núñez (2006)

Czechoslovak Mathematical Journal

In this paper we use cohomology of Lie algebras to study the variety of laws associated with filiform Lie algebras of a given dimension. As the main result, we describe a constructive way to find a small set of polynomials which define this variety. It allows to improve previous results related with the cardinal of this set. We have also computed explicitly these polynomials in the case of dimensions 11 and 12.

Abelian complex structures on 6-dimensional compact nilmanifolds

Luis A. Cordero, Marisa Fernández, Luis Ugarte (2002)

Commentationes Mathematicae Universitatis Carolinae

We classify the 6 -dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure J we describe the space of symplectic forms which are compatible with J .

About a family of naturally graded no p-filiform Lie algebras.

L. M. Camacho, J. R. Gómez, A. J. González (2005)

Extracta Mathematicae

The knowledge of the natural graded algebras of a given class of Lie algebras offers essential information about the structure of the class. So far, the classification of naturally graded Lie algebras is only known for some families of p-filiform Lie algebras. In certain sense, if g is a naturally graded Lie algebra of dimension n, the first case of no p-filiform Lie algebras it happens when the characteristic sequence is (n-3,2,1). We present the classification of a particular family of these algebras...

An extension of Mahler's theorem to simply connected nilpotent groups

Martin Moskowitz (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This Note gives an extension of Mahler's theorem on lattices in R n to simply connected nilpotent groups with a Q -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.

An obstruction to represent abelian Lie algebras by unipotent matrices.

J. C. Benjumea, F. J. Echarte, Núñez, J.,Tenorio, A. F. (2004)

Extracta Mathematicae

The aim of this paper is the study of abelian Lie algebras as subalgebras of the nilpotent Lie algebra gn associated with Lie groups of upper-triangular square matrices whose main diagonal is formed by 1. We also give an obstruction to obtain the abelian Lie algebra of dimension one unit less than the corresponding to gn as a Lie subalgebra of gn. Moreover, we give a procedure to obtain abelian Lie subalgebras of gn up to the dimension which we think it is the maximum.

An overview of free nilpotent Lie algebras

Pilar Benito, Daniel de-la-Concepción (2014)

Commentationes Mathematicae Universitatis Carolinae

Any nilpotent Lie algebra is a quotient of a free nilpotent Lie algebra of the same nilindex and type. In this paper we review some nice features of the class of free nilpotent Lie algebras. We will focus on the survey of Lie algebras of derivations and groups of automorphisms of this class of algebras. Three research projects on nilpotent Lie algebras will be mentioned.

Analytic joint spectral radius in a solvable Lie algebra of operators

Daniel Beltiţă (2001)

Studia Mathematica

We introduce the concept of analytic spectral radius for a family of operators indexed by some finite measure space. This spectral radius is compared with the algebraic and geometric spectral radii when the operators belong to some finite-dimensional solvable Lie algebra. We describe several situations when the three spectral radii coincide. These results extend well known facts concerning commuting n-tuples of operators.

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