0-dialgebras with bar-unity and nonassociative Rota--Baxter algebras.
A Leibniz algebra structure on the second tensor power.
A non-abelian tensor product of Leibniz algebra
Leibniz algebras are a non-commutative version of usual Lie algebras. We introduce a notion of (pre)crossed Leibniz algebra which is a simultaneous generalization of notions of representation and two-sided ideal of a Leibniz algebra. We construct the Leibniz algebra of biderivations on crossed Leibniz algebras and we define a non-abelian tensor product of Leibniz algebras. These two notions are adjoint to each other. A (co)homological characterization of these new algebraic objects enables us to...
Algèbres de Leibnitz : définitions, propriétés
Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras.
In this work the properties of Cartan subalgebras and weight spaces of finite dimensional Lie algebras are extended to the case of Leibniz algebras. Namely, the relation between Cartan subalgebras and regular elements are described, also an analogue of Cartan s criterion of solvability is proved.
Central series for groups with action and Leibniz algebras.
Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a
We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p − 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras.
Conformal representations of Leibniz algebras.
CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.
Dialgebras and related triple systems.
Existentially closed Leibniz algebras and an embedding theorem
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
Extensiones centrales de las álgebras de Leibniz.
Growth of some varieties of Leibniz-Poisson algebras
2010 Mathematics Subject Classification: 17A32, 17B63.Let V be a variety of Leibniz-Poisson algebras over an arbitrary field whose ideal of identities contains the identities {{x1,y1},{x2,y2},ј,{xm,ym}} = 0, {x1,y1}·{x2,y2}· ј ·{xm,ym} = 0 for some m. It is shown that the exponent of V exists and is an integer.
Künneth-style formula for the homology of Leibniz algebras.
Left-right noncommutative Poisson algebras
The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as...
Leibniz -algebras
A finite-dimensional Lie algebra is called an -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.
Leibniz cohomology for differentiable manifolds
We propose a definition of Leibniz cohomology, , for differentiable manifolds. Then becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of reduce to those of formal vector fields, and can be identified with certain invariants of foliations.
On Leibniz algebras with maximal cyclic subalgebras
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
On some anticyclic operads.
On some classes of nilpotent Leibniz algebras.