Related papers: More non semigroup Lie gradings

In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The…

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In…

Minimal Q-graded subalgebras of semisimple Lie algebras are introduced, and it is proved that their derived algebras are abelian. Almost inner derivations of minimal Q-graded subalgebras are investigated, they are all inner derivations.…

For most complex 9-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank $\geq 1$, only the characteristically nilpotent ones…

In this study, we extend the result on classification of a subclass of filiform Leibniz algebras in low dimensions to dimensions seven and eight based on the technique used by Rakhimov and Bekbaev for classification of subclasses which…

By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we calculate all of the second cohomology group of…

In this note, we describe some desingularizations of some subvarieties of the cartesian powers of a semisimple Lie algebra of finite dimension.

Let $\Gamma$ be a lattice in a simply-connected nilpotent Lie group $N$ whose Lie algebra $\mathfrak{n}$ is $p$-filiform. We show that $\Gamma$ is either abelian or 2-step nilpotent if $\Gamma$ is isomorphic to the fundamental group of a…

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra $\mathfrak{g}$, we describe the space of complex structures on…

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.

We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical…

We prove that any 2-generated minimal Taylor algebra on a domain of size 4 is not simple. In addition, we find all such algebras up to isomorphism and term-equivalence.

In math.DG/0312243 we developed a general classification scheme for metric Lie algebras, i.e. for finite-dimensional Lie algebras equipped with a non-degenerate invariant inner product. Here we determine all nilpotent Lie algebras l with…

In this article studies questions about the existence of left-invariant K\"{a}hler and semi-para-K\"{a}hler structures on six-dimensional unsolvable Lie groups whose Lie algebras are semidirect products. According to the classification…

We investigate the existence of left-invariant closed G$_2$-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a…

Borrowing some terminology from pro-p groups, thin Lie algebras are N-graded Lie algebras of width two and obliquity zero, generated in degree one. In particular, their homogeneous components have degree one or two, and they are termed…

The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple structure such as invariant function times…

A new kind of graded Lie algebra (we call it $Z_{2,2}$ graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable bose subspace of the $Z_{2,2}$ graded Lie algebra and using relevant…

We classify finite dimensional $H_{m^2}(\zeta)$-simple $H_{m^2}(\zeta)$-module Lie algebras $L$ over an algebraically closed field of characteristic $0$ where $H_{m^2}(\zeta)$ is the $m$th Taft algebra. As an application, we show that…

In this paper we study Lie 2-algebras over an algebraically closed field of characteristic two, which have a triangulable Cartan subalgebra, and derive some general properties of centerless ones. These properties allow us to do an analysis…