Example 2
Tag 09TR, permanent. Cite it as [Bourbaki, Tag 09TR].
Lie Groups and Lie Algebras, chapter I, § 1. Definition of Lie algebras
If a real Lie group G is commutative, its Lie algebra is commutative.
Every K-module can obviously be given a unique commutative Lie algebra structure over K.
If g is a Lie algebra, every monogenous submodule of g is a commutative Lie subalgebra of g.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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