Related papers: Supernilpotence prevents dualizability

First we describe the Skjelbred-Sund method for classifying nilpotent Lie algebras. Then we use it to classify 6-dimensional nilpotent Lie algebras over any field of characteristic not 2. The proof of this classification is essentially…

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…

The description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra is already known. Unfortunately, a mistake was made in that description. Namely, in the case where the dimension of the solvable…

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on…

The subpower membership problem SMP(A) of a finite algebraic structure A asks whether a given partial function from A^k to A can be interpolated by a term operation of A, or not. While this problem can be EXPTIME-complete in general,…

In this work, we extend the central extension method for solvable Leibniz algebras. Using this method, a complete classification of one-dimensional abelian extensions of five-dimensional solvable Leibniz algebras with a non-trivial…

Perez-Izquierdo and Shestakov recently extended the PBW theorem to Malcev algebras. It follows from their construction that for any Malcev algebra $M$ over a field of characteristic $\ne 2, 3$ there is a representation of the universal…

Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable…

In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms. In particular, we describe the complex and the real case of the indecomposable…

There are some results on nilpotent Lie algebras $ L $ investigate the structure of $ L $ rely on the study of its $2$-nilpotent multiplier. It is showed that the dimension of the $2$-nilpotent multiplier of $ L $ is equal to $ \frac{1}{3}…

A (vector space) basis B of a Lie algebra is said to be very nilpotent if all the iterated brackets of elements of B are nilpotent. In this note, we prove a refinement of Engel's Theorem. We show that a Lie algebra has a very nilpotent…

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…

We investigate almost inner derivations of some finite-dimensional nilpotent Leibniz algebras. We show the existence of almost inner derivations of Leibniz filiform non-Lie algebras differing from inner derivations, we also show that the…

This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie…

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…

Let p be a prime number. We give the explicit structure of 2- nilpotent multiplier for each finite 2-generator p-group of class two. Moreover, 2-capable groups in that class are characterized.

We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of finite-dimensional algebras, mostly over infinite fields.…

The present article is part of a research program the aim of which is to find all indecomposable solvable extensions of a given class of nilpotent Lie algebras. Specifically in this article we consider a nilpotent Lie algebra n that is…

Clonoids are sets of finitary operations between two algebraic structures that are closed under composition with their term operations on both sides. We conjecture that, for finite modules $\mathbf A$ and $\mathbf B$ there are only finitely…

In this work, we investigate anti-derivations and biderivation of Leibniz algebras. We describe general form of anti-derivations and biderivations on null-filiform and filiform Leibniz algebras. Moreover, we show how to construct Leibniz…