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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.

Anon
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1 Answers1

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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 $0$.

MichalisN
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  • Yeah that makes sense. Thank you for the reply! – Anon Apr 17 '12 at 11:57
  • Maybe worth noting that far more generally (but as a consequence of this), any finite group with the discrete topology is a $0$-dimensional Lie group, and has the zero space as Lie algebra. – Torsten Schoeneberg Jul 25 '22 at 14:44