On Lie algebras of type F4 and Chevalley groups F4(K), E6(K), and 2E6(K) for fields K of characteristic two

Abstract

In this article, we give an elementary and self-contained approach to construct the Lie algebras of type over an arbitrary field K of characteristic two. The Lie algebras are represented as subalgebras of , where AK is a 27-dimensional vector space over K. The Lie algebras of type for fields K of characteristic two have been constructed by the authors, using the notion of M sets. Here we follow the same notion to give an easy and effective construction of the corresponding Chevalley groups , and . It is remarkable to mention that most of the available literature on Chevalley groups does not deal with fields of characteristic two. Hence, this work aims to contribute in this regard.