Right-invariant differential form
= Right-invariant differential form
A <differential form> $\alpha$ on a <Lie group> is right-invariant if $R_g^*\alpha=\alpha$ for every right translation $R_g(p)=pg$. A right <Maurer-Cartan form> is represented in a matrix group by $dg\,g^{-1}$, whereas the left version is $g^{-1}dg$. Its components supply a right-invariant coframe.