On split Leibniz algebras
type: Item
instance of: scholarly article
title: On split Leibniz algebras
zbMATH Open document ID: 1287.17003
author: José M. Sánchez-Delgado
author: Antonio J. Calderón Martín
published in: Linear Algebra and its Applications
publication date: 2012-03-19T00:00:00Z
review text: It is well known that the Leibniz algebras theory is a generalisation of the Lie algebras theory; because of this, it is common to move all the concepts and results from the original theory to the new theory to check whether they work properly or not. In this paper, the authors introduce the concept of split Leibniz algebra as a generalisation of the concept of split Lie algebra. Moreover, a new decomposition for this kind of algebras is given. This decomposition is obtained through connections of roots techniques. The last section of this paper studies the case of split Leibniz algebras of maximal length, in order to provide a characterisation of a subclass of the simple Leibniz algebras class. This goal is obtained again through connections of roots techniques.
reviewed by: Manuel Avelino Insua Hermo
Mathematics Subject Classification ID: 17A32
zbMATH DE Number: 6015664
zbMATH Keywords: infinite dimensional Leibniz algebra
zbMATH Keywords: split Leibniz algebra
zbMATH Keywords: maximal length grading
zbMATH Keywords: root
zbMATH Keywords: root space
MaRDI profile type: Publication
full work available at URL: j.laa.2011.02.046
OpenAlex ID: W2070147214
Wikidata QID: Q123258413
cites work: Leibniz algebras in characteristic \(p\).
cites work: Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras
cites work: Varieties of Nilpotent Complex Leibniz Algebras of Dimension Less than Five
cites work: \(n\)-dimensional filiform Leibniz algebras of length \((n-1)\) and their derivations
cites work: Q3655579
cites work: Description of finite dimensional nilpotent complex Leibniz algebras with maximal nilindex
cites work: Q4406613
cites work: Q3515857
cites work: On split Lie algebras with symmetric root systems
cites work: On simple split Lie triple systems
cites work: On Universal Central Extensions of Leibniz Algebras
cites work: Quasi-filiform Lie algebras of maximum length
cites work: Q4548037
cites work: Q3516496
cites work: On the toroidal Leibniz algebras
cites work: A noncommutative version of Lie algebras: Leibniz algebras
cites work: Q3590250
cites work: The structure of locally finite split Lie algebras
DOI: 10.1016/J.LAA.2011.02.046
description: scientific article; zbMATH DE number 6015664