On isomorphisms and invariants of finite dimensional complex filiform Leibniz algebras

In this article, we propose an approach classifying a class of filiform Leibniz algebras. The approach is based on algebraic invariants. The method allows to classify all filiform Leibniz algebras (including filiform Lie algebras) in a given fixed dimensional case

A cohomological approach for classifying nilpotent Leibniz algebras

In this paper a cohomological approach (the Skjelbred-Sund method)to classify nilpotent Leibniz algebras in low dimensional cases will be presented. We distinguish six isomorphism classes (one parametric family and five concrete) of three dimensional nilpotent Leibniz algebras and show that they exhaust all possible cases

On bornological semigroups

In this paper we introduce and study the concept of a bornological semigroup. This generalizes the theory of algebraic semigroup from the algebraic setting to the framework of bornological set. Working with bornological set allows to extend the scope of the latter theory considerably. In this paper we develop and introduce the concept of bornological semigroup and fundamental construction in the class of bornological semigroup and study some of their basic proprieties

On classification problem of Loday algebras

This is a survey paper on classification problems of some classes of algebras introduced by Loday around 1990s. In the paper the author intends to review the latest results on classification problem of Loday algebras, achievements have been made up to date, approaches and methods implemented

On quasi-Armendariz properties on skew polynomial rings

This paper deals with the quasi-Armendariz ring in general setting. We generalize the notions of quasi-Armendariz and α-skew Armendariz ring to quasi α-Armendariz and quasi α-skew Armendariz ring and investigate their properties. The notions of quasi α-Armendariz and quasi α-skew Armendariz rings are useful in understanding the relationships between annihilators of rings R and R[x;α]

On skew version of reversible rings.

The paper deals with �-reversible rings and their relationships with well known �-symmetric, �-Armendariz and �-semicommutative rings. We consider a skew version of some classes of rings with respect to a ring endomorphism�

On isomorphism criteria for Leibniz central extensions of a linear deformation of mu_n.

This paper deals with the classification problems of Leibniz central extensions of linear deformations of a Lie algebra. It is known that any n-dimensional filiform Lie algebra can be represented as a linear deformation of n-dimensional filiform Lie algebra μ n given by the brackets [e i, e 0] = e i+1, i = 0,1,⋯,n-2, in a basis {e 0, e 1,⋯,e n-1}. In this paper we consider a linear deformation of μ n and its Leibniz central extensions. The resulting algebras are Leibniz algebras, this class is denoted here by Ced(μ n). We choose an appropriate basis of Ced(μ n) and give general isomorphism criteria. By using the isomorphism criteria, one can classify the class Ced(μ n) for any fixed n. Two relevant maple programs are provided

2-Local derivations on finite-dimensional semi-simple Lie algebras

We prove that every 2-local derivation on a finite-dimensional semi-simple Lie algebra L over an algebraically closed field of characteristic zero is a derivation. We also show that a finite-dimensional nilpotent Lie algebra L with dim L ≥ 2 admits a 2-local derivation which is not a derivation

On some new properties of catalan numbers.

It is well known that Catalan Numbers are used in Mathematical Biology as Enumerating RNA secondary structures for finite points. In this paper, we present some new properties of the Catalan Numbers

On isomorphism classes and invariants of a subclass of low-dimensional complex filiform Leibniz algebras

The article aims to study the classification problem of low-dimensional complex filiform Leibniz algebras. It is known that filiform Leibniz algebras come out from two sources. The first source is a naturally graded non-Lie filiform Leibniz algebra, and another one is a naturally graded filiform Lie algebra. In this article, we classify a subclass of the class of filiform Leibniz algebras appearing from the naturally graded non-Lie filiform Leibniz algebra. We give complete classification and isomorphism criteria in dimensions 5–7. The method of classification is purely algorithmic. The isomorphism criteria are given in terms of invariant functions