Related papers: An Example of Constructing Versal Deformation for …
We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of Stitzinger and Towers in Lie algebras. We show several examples which illustrate the…
We study the structure of a Leibniz triple system $\mathcal{E}$ graded by an arbitrary abelian group $G$ which is considered of arbitrary dimension and over an arbitrary base field $\mathbb{K}$. We show that $\mathcal{E}$ is of the form…
Let $A$ be a finite dimensional unital commutative associative algebra and let $B$ be a finite dimensional vertex $A$-algebroid such that its Levi factor is isomorphic to $sl_2$. Under suitable conditions, we construct an indecomposable…
Aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which controls deformations of Hom-Leibniz algebra structure. The cohomology and the associated deformation theory for Hom-Leibniz algebras as…
We present a method to construct explicitly L-infinity algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy use of the operad machinery of the…
This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters. In the first, we described the…
All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
We study all possible deformations of the Maxwell algebra. In D=d+1\neq 3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs…
We consider a vector space V over K=R or C, equipped with a skew symmetric bracket [.,.]: V x V --> V and a 2-form omega:V x V --> K. A simple change of the Jacobi identity to the form…
The paper concerns the classification problem of a subclass of complex filiform Leibniz algebras in dimensions 7 and 8. This subclass arises from naturally graded filiform Lie algebras. We give a complete list of isomorphism classes of…
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…
In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal…
This paper is devoted to the complete algebraic classification of complex 5-dimensional nilpotent bicommutative algebras.
The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that…
In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras containing abelian subalgebras of codimension 1, solvable and supersolvable Leibniz…
In this paper we study cohomology and deformations of Jacobi-Jordan algebras. We develop their formal deformation theory. In particular, we introduce a method to construct a versal deformation for a given Jacobi-Jordan algebra, which can…
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…
Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan,…
We provide a classification, up to isomorphism, of four-dimensional ternary Leibniz algebras over an algebraically closed field of characteristic zero. For each non-abelian algebra in the classification, we explicitly determine its centroid…
Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative associative $ K$-algebra which is an integral domain. Denote by $R$ the fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of $\mathbb…