Revisiting the universal linear algebraic model for the characteristic two case

In a previous article, a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes. This formalism was independent from the underlying field, providing an extension and general approach to other fields, such as finite fields. Some steps were taken even for the characteristic $2$ case. In this article, we undertake the study of the characteristic $2$ case in more detail. In particular, the concept of virtual quadratic spaces is used, defined in a previous article by the author, and a similar result is achieved for finite fields of characteristic $2$ as for other fields. Some differences from the non-characteristic $2$ case are also pointed out.