Example

Tag 0A9H, permanent. Cite it as [Bourbaki, Tag 0A9H].

Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra

Suppose that $G$ is the Lie group defined by a complete normable space $E$ . Then $\mathrm{U}(G)$ is identified with $\mathrm{TS}(E)$ and the restriction $\theta_*$ to $\mathrm{U}(G)$ is identified with $\mathrm{TS}(T_e(\theta))$ (Differentiable and Analytic Manifolds, R, 13.2.4). Therefore, if $t \in \mathrm{TS}^s(E)$ , $t^\vee = (-1)^s t$ .

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

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Cites

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