A noncommutative version of Lie algebras: Leibniz algebras
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.
scientific article; zbMATH DE number 597694