Introduction to \(gb\)-triple systems
type: Item
instance of: scholarly article
title: Introduction to \(gb\)-triple systems
zbMATH Open document ID: 1305.17003
DOI: 10.1155/2014/738154
published in: ISRN Algebra
publication date: 2014-06-16T00:00:00Z
review text: From the introduction: In this paper the author enriches the family of triple systems by introducing the concept of \(gb\)-triple systems, presented as another generalization of Leibniz algebras with the particularity that, for all \(a,b\in \mathfrak g\), the map \(T: \mathfrak g\to \mathfrak g\), defined by \(T_{a,b}(x)=T(a,b,x)\), is a derivation of \(\mathfrak g\), a property of great importance in Nambu mechanics. Then he investigates some of their algebraic properties and provides a functorial connection with Leibniz algebras and Lie algebras.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 17A32
zbMATH DE Number: 6304842
Wikidata QID: Q59049052
author: Guy R. Biyogmam
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/738154
OpenAlex ID: W1583942259
cites work: \(n\)-Lie algebras
cites work: Lie and Jordan Triple Systems
cites work: Q4707477
cites work: A noncommutative version of Lie algebras: Leibniz algebras
cites work: On nilpotent Leibniz \(n\)-algebras
description: scientific article; zbMATH DE number 6304842