J Austral Math Soc Ser A 57 pp365--385, 1994.

On the Component Group of the Automorphism Group of a Lie Group

P. B. Chen and T. S. Wu

(Received 31 May 1990; revised 18 August 1992)

Abstract

Let G be a Lie group, G_° the connected component of G that contains the identity, and Aut G the group of all topological automorphisms of G. In the case when G/G_° is finite and G has a faithful representation, we obtain a necessary and sufficient condition for G so that Aut G has finitely many components in terms of the maximal central torus in G_°.

1991 AMS Subject Classification: primary 22E15; secondary 22D45

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Authors

P. B. Chen: Department of Mathematics and Computer Science, John Carroll University, University Heights, OH 44118, USA.
T. S. Wu: Department of Mathematics ans Statistics, Case Western Reserve University, Cleveland, OH 44106, USA.

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