Remark

Tag 0A1S, permanent. Cite it as [Bourbaki, Tag 0A1S].

Lie Groups and Lie Algebras, chapter II, § 1. Enveloping bigebra of a Lie algebra

If $x \in E$ and $c(x) = x' \otimes u + u \otimes x''$ , where $x', x''$ are in $E^+$ , then $x = \varepsilon(x').u + \varepsilon(u).x'' = x''$ ; similarly $x = x'$ and $x$ is $u$ -primitive.

For all $x \in E^+$ , we write

(3)

c_u^+(x) = c(x) - x \otimes u - u \otimes x.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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