Classiffication of 4-dimensional nilpotent complex Leibniz algebras

Abstract

In [8] and [9] several classes of new algebras were introduced. Some of them have two generating operations and they are called dialgebras. The first motivation to introduce such algebraic structures (related with well known Lie and associative algebras) were problems in algebraic K-theory. The categories of these algebras over their operads assemble into the com- mutative diagram which re°ects the Koszul duality of those categories. The aim of the present paper is to study structural properties of one class of Lo- day's list, namely the so called Leibniz algebras. Leibniz algebras present a \non-commutative" (to be more precise, a \non- antisymmetric") analogue of Lie algebras.