Octonions, Albert vectors and the group ${}^2{\mathrm{E}}_6(F)$

John N. Bray, Yegor Stepanov, Robert A. Wilson

We extend the explicit octonionic approach to groups of type ${\mathrm{E}}_6$ to the twisted groups ${}^2{\mathrm{SE}}_{6,K}(F)$ associated with a quadratic Galois extension $K/F$. The…