Abelian Lie group
= Abelian Lie group
An abelian <Lie group> has commutative multiplication. Its <Lie algebra> is an <abelian Lie algebra>, and its <Lie exponential map> is a <group homomorphism> from the additive <Lie algebra>. Conversely, an additive <Lie exponential map> forces the <identity component of a Lie group> to be abelian, but does not force all disconnected components to commute.