On Lie algebras of type F ₄ and Chevalley groups F ₄ (K), E ₆ (K), and ² E ₆ (K) for fields K of characteristic two

In this article, we give an elementary and self-contained approach to construct the Lie algebras of type (Formula presented.) over an arbitrary field K of characteristic two. The Lie algebras are represented as subalgebras of (Formula presented.), where A _K is a 27-dimensional vector space over K. The Lie algebras of type (Formula presented.) 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 (Formula presented.), and (Formula presented.). 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.