scholarly journals Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length

2019 ◽  
Vol 47 (4) ◽  
pp. 1578-1594
Author(s):  
Kobiljon K. Abdurasulov ◽  
Jobir Q. Adashev ◽  
José M. Casas ◽  
Bakhrom A. Omirov
Keyword(s):  
Maximum Length ◽  
Leibniz Algebra ◽  
Leibniz Algebras ◽  
Filiform Leibniz Algebra

scholarly journals Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras

2021 ◽  
Author(s):  
Lucio Centrone ◽  
Chia Zargeh
Keyword(s):  
Hopf Algebra ◽  
Free Algebra ◽  
Hopf Algebras ◽  
Leibniz Algebra ◽  
Module Structure ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Filiform Leibniz Algebra ◽  
Algebra Over A Field ◽  
Cocommutative Hopf Algebra

AbstractLet L be an n-dimensional null-filiform Leibniz algebra over a field K. We consider a finite dimensional cocommutative Hopf algebra or a Taft algebra H and we describe the H-actions on L. Moreover we provide the set of H-identities and the description of the Sn-module structure of the relatively free algebra of L.

Some Properties of ID∗-n-Lie-derivations of Leibniz algebras

2021 ◽  
pp. 2250054
Author(s):  
G. R. Biyogmam ◽  
C. Tcheka ◽  
D. A. Kamgam
Keyword(s):  
Lie Algebra ◽  
Leibniz Algebra ◽  
Central Series ◽  
Algebra Structure ◽  
Leibniz Algebras ◽  
Lie Derivations

The concepts of [Formula: see text]-derivations and [Formula: see text]-central derivations have been recently presented in [G. R. Biyogmam and J. M. Casas, [Formula: see text]-central derivations, [Formula: see text]-centroids and [Formula: see text]-stem Leibniz algebras, Publ. Math. Debrecen 97(1–2) (2020) 217–239]. This paper studies the notions of [Formula: see text]-[Formula: see text]-derivation and [Formula: see text]-[Formula: see text]-central derivation on Leibniz algebras as generalizations of these concepts. It is shown that under some conditions, [Formula: see text]-[Formula: see text]-central derivations of a non-Lie-Leibniz algebra [Formula: see text] coincide with [Formula: see text]-[Formula: see text]-[Formula: see text]-derivations, that is, [Formula: see text]-[Formula: see text]-derivations in which the image is contained in the [Formula: see text]th term of the lower [Formula: see text]-central series of [Formula: see text] and vanishes on the upper [Formula: see text]-central series of [Formula: see text] We prove some properties of these [Formula: see text]-[Formula: see text]-[Formula: see text]-derivations. In particular, it is shown that the Lie algebra structure of the set of [Formula: see text]-[Formula: see text]-[Formula: see text]-derivations is preserved under [Formula: see text]-[Formula: see text]-isoclinism.

scholarly journals Racks, Leibniz algebras and Yetter–Drinfel'd modules

2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Ulrich Krähmer ◽  
Friedrich Wagemann
Keyword(s):  
Hopf Algebra ◽  
Leibniz Algebra ◽  
Unified Framework ◽  
Leibniz Algebras ◽  
Linear Maps

AbstractA Hopf algebra object in Loday and Pirashvili's category of linear maps entails an ordinary Hopf algebra and a Yetter–Drinfel'd module. We equip the latter with a structure of a braided Leibniz algebra. This provides a unified framework for examples of racks in the category of coalgebras discussed recently by Carter, Crans, Elhamdadi and Saito.

scholarly journals A study of n-Lie-isoclinic Leibniz algebras

2019 ◽  
Vol 19 (01) ◽  
pp. 2050013
Author(s):  
G. R. Biyogmam ◽  
J. M. Casas
Keyword(s):  
Leibniz Algebra ◽  
Leibniz Algebras

In this paper, we introduce the concept of [Formula: see text]-[Formula: see text]-isoclinism on non-Lie Leibniz algebras. Among the results obtained, we provide several characterizations of [Formula: see text]-[Formula: see text]-isoclinic classes of Leibniz algebras. Also, we provide a characterization of [Formula: see text]-[Formula: see text]-stem Leibniz algebras, and prove that every [Formula: see text]-[Formula: see text]-isoclinic class of Leibniz algebras contains a [Formula: see text]-[Formula: see text]-stem Leibniz algebra.

VARIETIES OF METABELIAN LEIBNIZ ALGEBRAS

2002 ◽  
Vol 01 (01) ◽  
pp. 31-50 ◽  
Author(s):  
VESSELIN DRENSKY ◽  
GIULIA MARIA PIACENTINI CATTANEO
Keyword(s):  
Systematic Study ◽  
Leibniz Algebra ◽  
Complete List ◽  
Asymptotic Description ◽  
Leibniz Algebras

In this paper we commence the systematic study of T-ideals of the free Leibniz algebra or, equivalently, varieties of Leibniz algebras, over a field of characteristic 0. We give a description of the free metabelian (i.e. solvable of class 2) Leibniz algebras, a complete list of all left-nilpotent of class 2 varieties and the asymptotic description of the metabelian varieties.

scholarly journals p -Filiform Leibniz algebras of maximum length

2014 ◽  
Vol 450 ◽  
pp. 316-333 ◽  
Author(s):  
L.M. Camacho ◽  
E.M. Cañete ◽  
J.R. Gómez ◽  
B.A. Omirov
Keyword(s):  
Maximum Length ◽  
Leibniz Algebras

Lie triple systems and Leibniz algebras

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Revaz Kurdiani
Keyword(s):  
Lie Algebra ◽  
Central Extension ◽  
Triple System ◽  
Leibniz Algebra ◽  
Universal Central Extension ◽  
Central Extensions ◽  
Lie Triple System ◽  
Triple Systems ◽  
Leibniz Algebras ◽  
Universal Central Extensions

AbstractThe present paper deals with the Lie triple systems via Leibniz algebras. A perfect Lie algebra as a perfect Leibniz algebra and as a perfect Lie triple system is considered and the appropriate universal central extensions are studied. Using properties of Leibniz algebras, it is shown that the Lie triple system universal central extension is either the universal central extension of the Leibniz algebra or the universal central extension of the Lie algebra.

scholarly journals Leibniz algebras, having a dense family of ideals

2020 ◽  
Vol 12 (2) ◽  
pp. 451-460
Author(s):  
N.N. Semko ◽  
L.V. Skaskiv ◽  
O.A. Yarovaya
Keyword(s):  
Leibniz Algebra ◽  
Leibniz Algebras

We say that a Leibniz algebra $L$ has a dense family of ideals, if for every pair of subalgebras $A$, $B$ of $L$ such that $A\leqslant B$ and $A$ is not maximal in $B$ there exists an ideal $S$ such that $A\leqslant S\leqslant B$. We study the Leibniz algebras, having a dense family of ideals.

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