Octonions, Albert vectors and the group E₆(F)

Abstract

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.

Keywords:

• Exceptional groups
• Jordan algebras
• octonions

2020 Mathematics Subject Classification:

• 20H20