3-filiform Lie algebras of dimension 8
A computer-based approach to the classification of nilpotent Lie algebras.
A conjecture on Lie algebras admitting a regular automorphism of finite order
A constructive method to determine the variety of filiform Lie algebras
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.
A nilpotent ideal in the Lie rings with automorphism of prime order.
A note on 2-step subideals of Lie algebras
A note on automorphism group of an n-generator nilpotent lie algebra
Abelian closure in soluble Lie rings
Abelian complex structures on 6-dimensional compact nilmanifolds
We classify the -dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure we describe the space of symplectic forms which are compatible with .
Abelian complex structures on solvable Lie algebras.
About a family of naturally graded no p-filiform Lie algebras.
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...
Algebras de Lie filiformes de máxima longitud.
Algèbres de Lie métabéliennes
Almost hermitian geometry on six dimensional nilmanifolds
Amalgams of Weyl algebras and the ... (V, ...) conjecture.
An extension of Mahler's theorem to simply connected nilpotent groups
This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
An improvement of a result of I. N. Stewart
An obstruction to represent abelian Lie algebras by unipotent matrices.
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
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
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.