Related papers: N-derivations for finitely generated graded Lie al…
A solvable Lie algebra L has the property that its nilradical N contains its own centraliser. This is interesting because gives a representation of L as a subalgebra of the derivation algebra of its nilradical with kernel equal to the…
We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives.
In this paper, we prove that every local derivation on Witt algebras $W_n, W_n^+$ or $W_n^{++} $ is a derivation for any $n\in\mathbb{N}$. As a consequence, we obtain that every local derivation on a centerless generalized Virasoro algebra…
In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular,the derivation algebras, the automorphism groups and the second cohomology groups of these…
In the present paper we prove the existence outer derivations finite-dimensional solvable Lie algebras with nilradical of maximal rank and complementary subspace to nilardical of dimension less than rank of the nilradical.
We investigate generalized derivations of $n$-BiHom-Lie algebras. We introduce and study properties of derivations, $( \alpha^{s},\beta^{r}) $-derivations and generalized derivations. We also study quasiderivations of $n$-BiHom-Lie…
We consider a class of infinite-dimensional, modular, graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. We identify two subclasses of Nottingham Lie…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
In general, the study of gradations has always represented a cornerstone in algebra theory. In particular, \textit{naturally graded} seems to be the first and the most relevant gradation when it comes to nilpotent algebras, a large class of…
A nilpotent Lie algebra ${\mathfrak g}$ is said to be naturally graded if it is isomorphic to its associated graded Lie algebra ${\rm gr} \mathfrak{g}$ with respect to filtration by ideals of the lower central series. This concept is…
This paper is devoted to investigating the structure theory of a class of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we completely determine the derivation algebras, the automorphism…
For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…
It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that…
In the paper we describe the derivations of complex $n$-dimensional naturally graded filiform Leibniz algebras $NGF_1, NGF_2\ \text{and} \ \ NGF_3.$ We show that the dimension of the derivation algebras of $NGF_1$ and $NGF_2$ equals $n+1$…
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
We study classical R-matrices D for Lie algebras L such that D is also a derivation of L. This yields derivation double Lie algebras (L,D). The motivation comes from recent work on post-Lie algebra structures on pairs of Lie algebras…
Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation…
We generalize the results of Leger and Luks about generalized derivations of Lie algebras to the case of color $n$-ary $\Omega$-algebras. Particularly, we prove some properties of generalized derivations of color $n$-ary algebras; prove…
Let $\mathfrak{g}$ be a real finite-dimensional Lie algebra containing pointed generating invariant closed convex cones. We determine those derivations $D$ of $\mathfrak{g}$ which induce a 3-grading of the form $\mathfrak{g} =…
Let $\mathbb K$ be an algebraically closed field of characteristic zero, $A = \mathbb K[x_1,\dots,x_n]$ the polynomial ring, and let $W_n(\mathbb K)$ denote the Lie algebra of all $\mathbb K$-derivations on $A$. The Lie algebra $W_n :=…