Related papers: On some basic properties of Leibniz algebras
The study of the Lefschetz properties of Artinian graded algebras was motivated by the hard Lefschetz theorem for a smooth complex projective variety, a breakthrough in algebraic topology and geometry. Over the last few years, this topic…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
A characterization of the finite-dimensional Leibniz algebras with an abelian subalgebra of codimension two over a field $\mathbb{F}$ of characteristic $p\neq2$ is given. In short, a finite-dimensional Leibniz algebra of dimension $n$ with…
Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove…
In this paper we find minimal faithful representations of several classes filiform Lie algebras by means of strictly upper-triangular matrices. We investigate Leibniz algebras whose corresponding Lie algebras are filiform Lie algebras such…
We prove Cuntz-Krieger and graded uniqueness theorems for Steinberg algebras. We also show that a Steinberg algebra is basically simple if and only if its associated groupoid is both effective and minimal. Finally we use results of…
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…
We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…
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.
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…
This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.
In this paper we prove that every irreducible representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also prove that - in general - for (semi)simple…
In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras, we also give the relations between elementary n-algebras and E-algebras.
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
In this paper, we mainly study the generalized Heisenberg-Virasoro algebra. Some structural properties of the Lie algebra are studied.
The concepts of derivations and right derivations for Leibniz algebras and $K$-B quasi-Jordan algebras naturally arise from the inner derivations determined by their algebraic structures. In this paper we introduce the corresponding…
In this paper, we introduce the concept of filter on IL-algebra. It is proved that this concept generalizes the notion of filter on Residuated Lattices. Prime filters on IL-algebra are defined and few interesting properties are obtained. It…
This paper aims at discussing the importance of Leibniz Law to getting models for Paraconsistent Set Theories.
We give an historical survey of some of the original basic algebraic and combinatorial results on Temperley-Lieb algebras, with a focus on certain results that have become folklore.
We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.