Article ID Journal Published Year Pages File Type
4587589 Journal of Algebra 2009 32 Pages PDF
Abstract

The long-root elements in Lie algebras of Chevalley type have been well studied and can be characterized as extremal elements, that is, elements x such that the image of 2(adx) lies in the subspace spanned by x. In this paper, assuming an algebraically closed base field of characteristic not 2, we find presentations of the Lie algebras of classical Chevalley type by means of minimal sets of extremal generators. The relations are described by simple graphs on the sets. For example, for Cn the graph is a path of length 2n, and for An the graph is the triangle connected to a path of length n−3.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory