Related papers: Lie bialgebra structures on 2-step nilpotent graph…

We study possible cases of complex simple graded Lie algebras of depth 2, which are the Tanaka prolongations of pseudo $H$-type Lie algebras arising through representation of Clifford algebras. We show that the complex simple Lie algebras…

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal…

We give an algebraic construction of the topological graph-tree configuration pairing of Sinha and Walter beginning with the classical presentation of Lie coalgebras via coefficients of words in the associative Lie polynomial. Our work…

Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6)(1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of loops on an orientable surface. Chas…

We continue the algebraic study of almost inner derivations of Lie algebras over a field of characteristic zero and determine these derivations for free nilpotent Lie algebras, for almost abelian Lie algebras, for Lie algebras whose…

Results about the following classes of finite-dimensional Lie algebras over a field of characteristic zero are presented: anisotropic (i.e., Lie algebras for which each adjoint operator is semisimple), regular (i.e., Lie algebras in which…

The aim of our paper is to construct pseudo $H$-type algebras from the covering free nilpotent two-step Lie algebra as the quotient algebra by an ideal. We propose an explicit algorithm of construction of such an ideal by making use of a…

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.

In this paper, we present recent results about the developement of a semiclassical approach in the setting of nilpotent Lie groups and nilmanifolds. We focus on two-step nilmanifolds and exhibit some properties of the weak limits of…

We consider pairs (V,H) of subgroups of a connected unipotent complex Lie group G for which the induced VxH-action on G by multiplication from the left and from the right is free. We prove that this action is proper if the Lie algebra g 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…

Oriented graph complexes, in which graphs are not allowed to have oriented cycles, govern for example the quantization of Lie bialgebras and infinite dimensional deformation quantization. It is shown that the oriented graph complex GC^or_n…

We classify 7-dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left-invariant purely coclosed $G_2$-structures. This is done by going through the list of all 7-dimensional nilpotent Lie algebras…

For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily computable necessary and sufficient conditions to…

The concept of breadth has been used in the classification of p-groups and nilpotent Lie algebras. In this paper, we investigate this notion for finite-dimensional solvable Lie algebras. Our main focus is to characterize solvable Lie…

Leibniz algebras are certain generalization of Lie algebras. In this paper we give the classification of four dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear…

Any abstract (not necessarily continuous) group automorphism of a simple, compact Lie group must be continuous due to Cartan (1930) and van der Waerden (1933). The purpose of this paper is to study a similar question in nilpotent Lie…

We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real…

We study almost inner derivations of $2$-step nilpotent Lie algebras of genus $2$, i.e., having a $2$-dimensional commutator ideal, using matrix pencils. In particular we determine all almost inner derivations of such algebras in terms of…

The paper is devoted to give the complete algebraic classification of nilpotent binary Lie algebras of dimension $\leq 6$ over an arbitrary base field ${\mathbb{F}}$ of characteristic not $2$ and the complete geometric classification of…