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.
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Acknowledgements
The first author would like to thank Kuwait Foundation for the Advancement of Sciences and PAAET for supporting project Nos. P115-16-SM, BE-15-13 respectively. The second author would like to thank H. J. Schaeefer, C. Hering and A. Alazemi for their remarks on this article.