Closed left-invariant 1-form
= Closed left-invariant 1-form
On a connected <Lie group>, a <left-invariant differential form>[left-invariant] <differential 1-form> is <closed differential form>[closed] exactly when it is <bi-invariant differential form>[bi-invariant]. Connectedness is essential: on $O(2)$ every left-invariant 1-form is closed because its Lie algebra is abelian, while reflection conjugation negates every nonzero one.