Related papers: A distinguished example of filiform deformation
For each complex 8-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 $\ge 1$, only the caracteristically nilpotent ones should…
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 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…
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…
The notion of singular one-parameter deformation of a Lie algebra is introduced. It is shown that the complex infinite-dimensional Lie algebra of polynomial vector fields in C with trivial 1-jet at the origin has such singular deformation.
We construct, for any integer n greater than or equal to 5, a family of complex filiform Lie algebras with derived length at most 3 and dimension n. We also give examples of n-dimensional filiform Lie algebras with derived length greater…
A finite dimensional filiform K-Lie algebra is a nilpotent Lie algebra g whose nil index is maximal, that is equal to dim g -1. We describe necessary and sufficient conditions for a filiform algebra over an algebraically closed field of…
In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra $\mathfrak{n}_3$ and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations. We also describe the versal…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e. filiform Lie (super)algebras, into the theory of Lie algebras of order F$. Thus, the concept of filiform Lie algebras of order F is…
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…
We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra.…
We give some examples of non-complete invariant affine connections on nilpotent and filiform Lie groups. This permits to describe non-nilpotent faithful representations on the model of filiform n-dimensional Lie algebras and, in particular,…
The classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given…
We classify the (n-5)-filiform Lie algebras which have the additional property of a non-abelian derived subalgebra. We show that this property is strongly related with the structure of the Lie algebra of derivations; explicitely we show…
We study symplectic structures on filiform Lie algebras -- nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the Lie algebras with the structure relations of the following…
In this work it is considered the vector space composed by the infinitesimal deformations of the model $\mathbb{Z}_3$-filiform Lie algebra $L^{n,m,p}$. By using these deformations all the $\mathbb{Z}_3$-filiform Lie algebras can be…
We prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low…
Denote m_0 the infinite dimensional N-graded Lie algebra defined by basis e_i, i>= 1 and relations [e_1,e_i] = e_(i+1) for all i>=2. We compute in this article the bracket structure on H1(m_0,m_0), H2(m_0,m_0) and in relation to this, we…
This article explores some simple examples of L-infinity algebras and the construction of miniversal deformations of these structures. Among other things, it is shown that there are two families of nonequivalent L-infinity structures on a…