A noncommutative version of Lie algebras: Leibniz algebras
type: Item
instance of: scholarly article
title: A noncommutative version of Lie algebras: Leibniz algebras
zbMATH Open document ID: 0806.55009
author: J.-L. Loday
published in: L'Enseignement Mathématique. 2e Série
publication date: 1994-07-19T00:00:00Z
review text: A Leibniz algebra over a commutative ring \(\mathbb{K}\) is a \(\mathbb{K}\)-module \(g\) together with a bilinear map \([-,-]: g\times g\to g\) satisfying for all \(x\), \(y\), \(z\) in \(G\), \([x, [y,z]] - [[x, y],z]+ [[x, z],y]=0\). The paper introduces this new algebraic structure and presents some interesting properties and connections with other theories. The main motivation is the existence of a homology theory \(HL_*\) that gives in particular new algebraic invariants for Lie algebras. This paper is clearly written and gives a lot of new and interesting questions in homological algebra.
Mathematics Subject Classification ID: 17A32
Mathematics Subject Classification ID: 17B55
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 19D55
zbMATH DE Number: 597694
zbMATH Keywords: Hochschild homology
zbMATH Keywords: Leibniz algebra
zbMATH Keywords: algebraic invariants for Lie algebras
reviewed by: Yves Félix
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 597694