Octonions, Albert vectors and the group ${\mathrm{E}}_6(F)$

Abstract

We present a uniform approach to the construction of the groups of type ${\mathrm{E}}_6$ over arbitrary fields without using Lie theory. This gives a simple description of the group generators and some of the subgroup structure. In the finite case our approach also permits relatively straightforward computation of the group order.

arXiv comment30 pages