About a family of naturally graded no p-filiform lie algebras

Junta de Andalucia, PAICYT y Ministerio de Ciencia y Tecnología BFM 2000-104

A historical review of the classifications of Lie algebras

The problem of Lie algebras’ classification, in their different varieties, has been dealt with by theory researchers since the early 20th century. This problem has an intrinsically infinite nature since it can be inferred from the results obtained that there are features specific to each field and dimension. Despite the hundreds of attempts published, there are currently fields and dimensions in which only partial classifications of some families of algebras of low dimensions have been obtained. This article intends to bring some order to the achievements of this prolific line of research so far, in order to facilitate future research

Solvable Leibniz algebras with triangular nilradicals

In this paper the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and right operators on elements of Leibniz algebra have upper triangular forms. We establish that solvable Leibniz algebra of a maximal possible dimension with a given triangular nilradical is a Lie algebra. Furthermore, solvable Leibniz algebras with triangular nilradicals of low dimensions are classified.Comment: 10 pages, Submitted to Linear Algebra and Its Applications(LAA) at 16.06.201

Solvable Leibniz algebras with triangular nilradical

A classification exists for Lie algebras whose nilradical is the triangular Lie algebra $T(n)$. We extend this result to a classification of all solvable Leibniz algebras with nilradical $T(n)$. As an example we show the complete classification of all Leibniz algebras whose nilradical is $T(4)$.Comment: arXiv admin note: text overlap with arXiv:1307.844

Solvable Leibniz Algebras with Filiform Nilradical

In this paper we continue the description of solvable Leibniz algebras whose nilradical is a filiform algebra. In fact, solvable Leibniz algebras whose nilradical is a naturally graded filiform Leibniz algebra are described in [6] and [8]. Here we extend the description to solvable Leibniz algebras whose nilradical is a filiform algebra. We establish that solvable Leibniz algebras with filiform Lie nilradical are Lie algebras.Ministerio de Economía y Competitividad MTM2013-43687-

Can solvable extensions of a nilpotent subalgebra be useful in the classification of solvable algebras with the given nilradical?

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_{n,3} which contains the previously studied filiform nilpotent algebra n_{n-2,1} as a subalgebra but not as an ideal. Rather surprisingly it turns out that the classification of such solvable algebras can be reduced to the classification of solvable algebras with the nilradical n_{n-2,1} together with one additional case. Also the sets of invariants of coadjoint representation of n_{n,3} and its solvable extensions are deduced from this reduction. In several cases they have polynomial bases, i.e. the invariants of the respective solvable algebra can be chosen to be Casimir invariants in its enveloping algebra.Comment: 19 page