Quaternionic Reflections and Lie Generation in $G_2$

Santiago Pineda Montoya, Johan H. Rúa Muñoz, Borut Jurčič Zlobec

Let $\mathbb{O}$ be the real octonion division algebra and ${\mathfrak{g}}_2=\mathrm{Der}(\mathbb{O})$. A quaternionic reflection $T\in G_2=\mathrm{Aut}(\mathbb{O})$ fixes a…