Exercise 4, § 1

Tag 019T, permanent. Cite it as [Bourbaki, Tag 019T].

Lie Groups and Lie Algebras, IX, 389

Show that the conditions in Prop. 3 (no. 3) are equivalent to each of the following conditions:

(ii $'$ ) The group Ad(G) is relatively compact in Aut(L(G)).

(ii $''$ ) The group Ad(G) is relatively compact in End(L(G)). (v) Every neighbourhood of the identity element $e$ of G contains a neighbourhood of $e$ stable under inner automorphisms (cf. Integration, §3, no. 1, Prop. 1).

Solution

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Cites

Integration, §3, no. 1, Prop. 1 not in this corpus: INT
Prop. 3