Related papers: Half-flat structures on indecomposable Lie groups

Let $\mathfrak{g}$ be a $2n$-dimensional unimodular Lie algebra equipped with a Hermitian structure $(J,F)$ such that the complex structure $J$ is abelian and the fundamental form $F$ is balanced. We prove that the holonomy group of the…

Given a finite connected bipartite graph, finite-dimensional indecomposable semisimple Leibniz algebras are constructed. Furthermore, any finite-dimensional indecomposable semisimple Leibniz algebra admits a similar construction.

We investigate Lie algebras whose Lie bracket is also an associative or cubic associative multiplication to characterize the class of nilpotent Lie algebras with a nilindex equal to 2 or 3. In particular we study the class of 2-step…

Let L be a Lie pseudoalgebra, a in L. We show that, if a generates a (finite) solvable subalgebra S=<a>, then one may find a lifting a' in S of [a] in S/S' such that <a'> is nilpotent. We then apply this result towards vertex algebras: we…

We study post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$, motivated by nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic…

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded $p$-filiform non-Lie Leibniz algebra $(n-p\geq4)$ and the…

The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that any 2-step nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is a 2-step…

We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…

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…

It is known that there exist complex solvmanifolds $(\Gamma\backslash G,J)$ whose canonical bundle is trivialized by a holomorphic section which is not invariant under the action of $G$. The main goal of this article is to classify the…

In this paper we study metric deformations of indecomposable metric Lie superalgebras with dimensions less or equal to 6. We consider formal deformations obtained by even cocycles, because the odd ones can not be used for constructing…

In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use this method to obtain the algebraic classification of complex…

We determine normal forms of the multiplication of four-dimensional anti-commutative algebras over a field $\mathbb K$ of characteristic zero having an analogous family of flags of subalgebras as the four-dimensional non-Lie binary Lie…

We investigate a certain class of solvable metric Lie algebras. For this purpose a theory of twofold extensions associated to an orthogonal representation of an abelian Lie algebra is developed. Among other things, we obtain a…

In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated…

It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…

A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants…

For a finite dimensional Lie algebra $L$, it is known that $s(L)=\f{1}{2}(n-1)(n-2)+1-\mathrm{dim} M(L)$ is non negative. Moreover, the structure of all finite nilpotent Lie algebras is characterized when $s(L)=0,1$ in \cite{ni,ni4}. In…

We compute the torsion-free linear maps from the Lie algebra su(2) into itself, deduce a new determination of the integrable complex structures and their equivalence classes under the action of the automorphism group for u(2) and…

We study bi-Lagrangian structures (a symplectic form with a pair of complementary Lagrangian foliations, also known as para-K\"ahler or K\"unneth structures) on nilmanifolds of dimension less than or equal to 6. In particular, building on…