A geometry of the generalized quadrangle (Ω,𝔏) of type O6−(2) and Lie algebras of type E6 with characteristic two.

The purpose of this paper is to study certain geometric properties of generalized quadrangle (Ω , 𝔏) of type O 6 − (2). We define certain root elements which generate a Lie algebra of type E 6 (K) for fields K of characteristic two. The construction will be mainly based on the geometric properties of the generalized quadrangle (Ω , 𝔏). In fact, we will explicity construct a Chevalley base of this Lie algebra. [ABSTRACT FROM AUTHOR]