Related papers: Novikov structures on solvable Lie algebras
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a $2$-step solvable Lie algebra without…
We study ideals of Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We present the first example of a three-step nilpotent Lie algebra which does not admit a Novikov structure. On the other hand we show that any…
In the study of NIL-affine actions on nilpotent Lie groups we introduced so called LR-structures on Lie algebras. The aim of this paper is to consider the existence question of LR-structures, and to start a structure theory of LR-algebras.…
We prove that any Novikov algebra over a field of characteristic $\neq 2$ is Lie-solvable if and only if its commutator ideal $[N,N]$ is right nilpotent. We also construct examples of infinite-dimensional Lie-solvable Novikov algebras $N$…
We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\frak a \frak f \frak f (A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural…
We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional…
In this work, the complex Lie affgebra structures on three-dimensional solvable Lie algebras are completely determined.
Novikov algebras are algebras whose associators are left-symmetric and right multiplication operators are mutually commutative. A Gel'fand-Dorfman bialgebra is a vector space with a Lie algebra structure and a Novikov algebra structure,…
We present a new look at description of real finite-dimensional Lie algebras. The basic element turns out to be a pair $(F,v)$ consisting of a linear mapping $F\in End(V)$ and its eigenvector $v$. This pair allows to build a Lie bracket on…
We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step…
In this paper we study some affine structures on nilpotent Lie algebras endowed with a contact form. These affine structures are constructed from an affine structure on a symplectic Lie algebra by a central extension.
In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.
The complete affine structures on abelian Lie algebras in small dimensions are well known. In this paper we are interested by the non complete case. In particular we classify all these structures in dimensions 2 and 3.
In this paper, the structure of all finite-dimensional nilpotent Lie algebras of class two with derived subalgebra of dimension two over an arbitrary field $ \mathbb{F} $ is determined. Furthermore, we give the structure of the Schur…
This work investigates the existence of complex structures on 2-step nilpotent Lie algebras arising from finite graphs. We introduce the notion of adapted complex structure, namely a complex structure that maps vertices and edges of the…
We study the algebraic constraints on the structure of nilpotent Lie algebra $\mathbb{g}$, which arise because of the presence of an integrable complex structure $J$. Particular attention is paid to non-abelian complex structures.…
We introduce post-Lie algebra structures on pairs of Lie algebras $(\Lg,\Ln)$ defined on a fixed vector space $V$. Special cases are LR-structures and pre-Lie algebra structures on Lie algebras. We show that post-Lie algebra structures…
We define a solvable extension of the graph 2-step nilpotent Lie algebras of [5] by adding elements corresponding to the 3-cliques of the graph. We study some of their basic properties and we prove that two such Lie algebras are isomorphic…
Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to…