= Scaled right Maurer-Cartan gauge potential
{title2=$F_{xy}=\alpha(1+\alpha)[B_x,B_y]$}
Write $B_i=(\partial_i g)g^{-1}$ and use $D=d+A$. The right <Maurer-Cartan equation> gives $\partial_xB_y-\partial_yB_x=[B_x,B_y]$. Thus $A_i=\alpha B_i$ has the displayed <gauge curvature>. Both $\alpha=0$ and $\alpha=-1$ are universally flat; the latter is a <pure gauge potential>. Commuting $B_x,B_y$ give additional flat cases. For the opposite convention $D=d-A$, the corresponding component formula instead has $\alpha(1-\alpha)$.
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