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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.

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up vote 3 down vote accepted

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 $0$.

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Yeah that makes sense. Thank you for the reply! – Alex Kite Apr 17 '12 at 11:57

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