Bourbaki

Corollary 2

Tag 039I, permanent. Cite it as [Bourbaki, Tag 039I].

Théories spectrales, chapter V, § 1. Représentations unitaires

Every finite-dimensional unitary representation ϱ\varrho of a topological group G is semisimple.

This follows from Prop. 7 and Lemma 3 of V, p. 379.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

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Machine translation of the English, by gpt-5.4, gpt-5-6-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.