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(Just testing -- pay no attention to the man behind the curtain.)
${{G}_{-}}\cong {{N}_{-}}\times (U(n-1)\times {{\mathbb{R}}^{+}})$. Note the analogy with the Euclidean similarity group $\text{Sim}({{\mathbb{R}}^{2n+1}})={{\mathbb{R}}^{2n+1}}\times (\mathrm{O}(2n+1)\times {{\mathbb{R}}^{+}})$.
(Just testing -- pay no attention to the man behind the curtain.)
${{G}_{-}}\cong {{N}_{-}}\times (U(n-1)\times {{\mathbb{R}}^{+}})$. Note the analogy with the Euclidean similarity group $\text{Sim}({{\mathbb{R}}^{2n+1}})={{\mathbb{R}}^{2n+1}}\times (\mathrm{O}(2n+1)\times {{\mathbb{R}}^{+}})$.
[{{\mathfrak{n}}_{-}}=\left{ \left[ \begin{matrix} {{0}_{n-1}} & \zeta & \zeta \ -{{\zeta }^{}} & -iv & -iv \ {{\zeta }^{}} & iv & iv \ \end{matrix} \right],\zeta \in {{\mathbb{C}}^{n-1}},v\in \mathbb{R} \right}]
(Just testing -- pay no attention to the man behind the curtain.)
${{G}_{-}}\cong {{N}_{-}}\times (U(n-1)\times {{\mathbb{R}}^{+}})$. Note the analogy with the Euclidean similarity group $\text{Sim}({{\mathbb{R}}^{2n+1}})={{\mathbb{R}}^{2n+1}}\times (\mathrm{O}(2n+1)\times {{\mathbb{R}}^{+}})$.
[{{\mathfrak{n}}_{-}}=\left{ \left[ \begin{matrix} {{0}_{n-1}} & \zeta & \zeta \ -{{\zeta }^{}} & -iv & -iv \ {{\zeta }^{}} & iv & iv \ \end{matrix} \right],\zeta \in {{\mathbb{C}}^{n-1}},v\in \mathbb{R} \right}]
(Just testing -- pay no attention to the man behind the curtain.)
${{G}_{-}}\cong {{N}_{-}}\times (U(n-1)\times {{\mathbb{R}}^{+}})$. Note the analogy with the Euclidean similarity group $\text{Sim}({{\mathbb{R}}^{2n+1}})={{\mathbb{R}}^{2n+1}}\times $\operatorname{Sim}({{\mathbb{R}}^{2n+1}})={{\mathbb{R}}^{2n+1}}\times (\mathrm{O}(2n+1)\times {{\mathbb{R}}^{+}})$.