Generating pairs in ${\mathfrak{g}}_2$ related by an involution

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

Let $\mathbb{O}$ be the real octonion division algebra, let ${\mathfrak{g}}_2=\mathrm{Der}(\mathbb{O})$, and fix a quaternionic subalgebra $H\subset \mathbb{O}$. We ask when an elem…