Vol. 32, No. 1, 1970

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The adjoint group of Lie groups

Dong Hoon Lee

Vol. 32 (1970), No. 1, 181–186

Let G be a Lie group and let Aut(G) denote the group of automorphisms of G. If the subgroup Int (G) of innerautomorphisms of G is closed in Aut (G), then we call G a (CA) group (after Van Est.). In this note, we investigate (CA) property of certain classes of Lie groups. The main results are as follows: THEOREM A. Let G be an analytic group and suppose that there is no compact semisimple normal subgroup of G. If G contains a closed uniform (CA) subgroup H, then G is (CA). THEOREM B. If G is an analytic group whose exponential map is surjective, then G is (CA).

Mathematical Subject Classification
Primary: 22.50
Received: 28 July 1969
Published: 1 January 1970
Dong Hoon Lee