Let $L$ be a finite dimensional Lie algebra over $\mathbb{R}$, and $K$ a subalgebra of $L$. Then, by Lie's correspondence theorems, there exists a unique (up to isomorphisms) simply connected Lie group $G$ having $L$ as a Lie algebra. There also exists a unique connected Lie subgroup $H$ of $G$ having $K$ as its Lie algebra.


Question: What algebraic condition on the pair $(L, K)$ determines if $H$ will be an embedded submanifold or not?



Algebraic condition that distinguishes embedded from immersed lie subgroups
See the [closed-subgroup theorem](https://www.wikiwand.com/en/Closed-subgroup_theorem), in particular the [conditions for being closed](https://www.wikiwand.com/en/Closed-subgroup_theorem#Conditions_for_being_closed).


