The Lie Algebra of a trivial Lie Group

Question

I was wondering if it is true that the lie algebra of a trivial lie group is trivial? Surely the answer is yes but I just want to make sure.

Answer 1

You can see the trivial group as a 0-dimensional manifold. The corresponding Lie-algebra is defined as $T_e G$, which, seen as a vector space has the dimension of the manifold, hence $0$.