DIGROUPS AND THEIR LINEAR PRESENTATIONS

Abstract

In this paper we introduce the notion of digroup. It constitutes a version of the concept of group for sets with two products, such that, each element has an inverse which is the same for the two products. The basic results of the digroups are proved and some open problems are enunciated. Also, it is presented an approach of the representation theory for digroups where the notion of regular vector in Leibniz algebras, introduced recently by the author (see [3]), has a fundamental role.