Remark 1

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

Lie Groups and Lie Algebras, chapter VI, § 3. Exponential invariants

If 2 is not a zero divisor in $A$ , it is easy to check that $d$ is the unique anti-invariant element of $A[P]$ with $e^\rho$ as its maximal term.

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

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