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On the component group of the automorphism group of a Lie group

Part of: Locally compact groups and their algebras Lie groups

Published online by Cambridge University Press:  09 April 2009

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

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Let G be a Lie group, Go 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/Go 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 Go.

MSC classification

Secondary: 22E15: General properties and structure of real Lie groups 22D45: Automorphism groups of locally compact groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 3 , December 1994 , pp. 365 - 385
Copyright
Copyright © Australian Mathematical Society 1994

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