相关论文: Cohomologically rigid solvable Lie superalgebras w…
We construct large families of characteristically nilpotent Lie algebras by considering deformations of the Lie algebra g_{m,m-1}^{4} of type Q_{n},and which arises as a central extension fo the filiform Lie algebra L_{n}. By studying the…
Along this paper we show that under certain conditions the method for describing of solvable Lie and Leibniz algebras with maximal codimension of nilradical is also extensible to Lie and Leibniz superalgebras, respectively. In particular,…
In this work, we recall that every filiform Lie superalgebra is a deformation of the superalgebra $L_{n,m}$. We study the even cocycles which give this nilpotent deformations. A family of independent bilinear maps will help us to describe…
Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable…
We extend the classical construction of solvable Lie algebras from a nilradical to compatible Lie algebras. Since the sum of nilpotent ideals may fail to be nilpotent, we replace the usual nilradical by a \emph{special nilradical} that…
All finite-dimensional indecomposable solvable Lie algebras g, having the filiform Lie algebra Q_(2m+1) as the nilradical, are studied and classified. It turns out that the dimension of g is at most dimQ_(2m+1)+2.
In this work we consider extensions of solvable Lie algebras with naturally graded filiform nilradicals. Note that there exist two naturally graded filiform Lie algebras $n_{n, 1}$ and $Q_{2n}.$ We find all one-dimensional central…
All finite-dimensional indecomposable solvable Lie algebras $L(n,f)$, having the triangular algebra T(n) as their nilradical, are constructed. The number of nonnilpotent elements $f$ in $L(n,f)$ satisfies $1\leq f\leq n-1$ and the dimension…
We determine the solvable complete Lie algebras whose nilradical is isomorphic to a filiform Lie algebra. Moreover we show that for any positive integer $n$ there exists a solvable complete Lie algebras whose second cohomology group with…
In this paper we establish some basic properties of superderivations of Lie superalgebras. Under certain conditions, for solvable Lie superalgebras with given nilradicals, we give estimates for upper bounds to dimensions of complementary…
The description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra is already known. Unfortunately, a mistake was made in that description. Namely, in the case where the dimension of the solvable…
We give necessary conditions for the existence of degenerations between two complex Lie superalgebras of dimension $(m,n)$. As an application, we study the variety $\mathcal{LS}^{(2,2)}$ of complex Lie superalgebras of dimension $(2,2)$.…
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…
In this paper we introduce the notion of pure non-characteristically nilpotent Lie algebra and under a condition we prove that a complex maximal extension of a finite-dimensional pure non-characteristically nilpotent Lie algebra is…
In this paper solvable Leibniz algebras whose nilradical is quasi-filiform Lie algebra of maximum length, are classified. The rigidity of such Leibniz algebras with two-dimensional complemented space to nilradical is proved.
The present article is part of a research program the aim of which is to find all indecomposable solvable extensions of a given class of nilpotent Lie algebras. Specifically in this article we consider a nilpotent Lie algebra n that is…
We determine fundamental systems of invariants for complex solvable rigid Lie algebras having nonsplit nilradicals of characteristic sequence $(3,1,..,1)$, these algebras being the natural followers of solvable algebras having Heisenberg…
This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters. In the first, we described the…
The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable…
In this paper, we provide a complete description of complex maximal solvable extensions for a certain class of nilpotent Lie algebras. In particular, we show that, up to isomorphism, a solvable extension of a $d$-locally diagonalizable…