Remark 1

Tag 0A6B, permanent. Cite it as [Bourbaki, Tag 0A6B].

Lie Groups and Lie Algebras, chapter II, § 6. The Hausdorff series

If $a$ and $b$ commute, then $H_{r,s}(a, b) = 0$ for $r + s \geq 2$ , for every homogeneous Lie polynomial of degree $\geq 2$ is zero at $(a, b)$ . Then $H(a, b) = a + b$ and Proposition 3 recovers the formula

\exp(a + b) = \exp a . \exp b.

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

Cited by

Nothing.

Cites

Proposition 3