= Lie third theorem
{c}
{title2=$\operatorname{Lie}(H)\cong\mathfrak h$}
Every finite-dimensional real <Lie algebra> is the <Lie algebra> of a connected <simply connected> <Lie group>. One construction first uses the <Ado theorem> to embed it into a matrix <Lie algebra>, integrates the corresponding left-invariant distribution by the <Frobenius theorem> to a connected immersed <Lie subgroup>, and then takes a <universal covering Lie group>. The immersed <subgroup> need not be closed; taking its ambient closure may change its <Lie algebra>.
Back to article page
