$$\begin{aligned} \mathfrak{h}_{+} &=&\mathfrak{g}_{+}\oplus \mathfrak{g}_{+}^{\bot }=Lspan\left\{ \left( e_{0},0\right) ,\left( e_{0},0\right) ,\left( e_{0},0\right) ,\left( 0,e_{0}\right) ,\left( 0,e_{0}\right) \left( 0,e_{0}\right) \right\}