Flat translation connections on a Lie group
= Flat translation connections on a Lie group
{title2=$\nabla^-_XY=0,\quad\nabla^+_XY=[X,Y]$}
Declare a global left-invariant, respectively right-invariant, frame parallel to obtain two flat <affine connections> on a <Lie group>. For <left-invariant vector fields>, their derivatives are as displayed and their <torsion tensors> are $-[X,Y]$ and $+[X,Y]$. The tensors vanish on Abelian groups; two genuinely torsionful connections are not asserted there.