Non-linear Lie groups.

Question

We know that for a matrix Lie group $G$, we define it to be a closed subgroup of $GL(n,\mathbb{C})$. But Lie groups are defined as manifolds in $\mathbb{R}^n$ for some $n$, in general. The question is that, do we know any Lie group which is not a matrix Lie group? Thank you very much.

Answer 1

https://mathoverflow.net/questions/91789/non-linear-lie-group/91805#91805