Remark

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

Lie Groups and Lie Algebras, chapter III, § 6. Real and complex Lie groups

(1) There exist finite-dimensional simply connected Lie groups which have no finite-dimensional injective analytic linear representation (Exercise 2).

(2) There exist finite-dimensional connected Lie groups $G$ such that every finite-dimensional analytic linear representation of $G$ has non-discrete kernel (Exercises 3 and 4).

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

Cited by

Nothing.

Cites

Exercise 2