Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-02-03T17:01:57.219Z Has data issue: false hasContentIssue false
  • English
  • Français

On the automorphism group of a connected locally compact topological group

Published online by Cambridge University Press:  20 January 2009

Ta-Sun Wu
Ta-Sun Wu
Affiliation:
Case Western Reserve UniversityCleveland, Ohio 44106, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a locally compact connected topological group. Let Aut0G be the identity component of the group of all bi-continuous automorphisms of G topologized by Birkhoff topology. We give a necessary and sufficient condition for Aut0G to be locally compact.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 2 , June 1992 , pp. 285 - 294
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Chen, P. and Wu, T. S., On the automorphism groups of locally compact groups and on a theorem of M., Goto, Tamkang J. Math. 17 (1986), 99–116.Google Scholar
2.Chen, P. and Wu, T. S., On a class of topological groups, Math. Ann. 266 (1984), 499–506.CrossRefGoogle Scholar
3.Goto, M. and Kimura, N., Semigroup of endomorphisms of a locally compact group, Trans. Amer. Math. Soc. 87 (1958), 359–371.CrossRefGoogle Scholar
4.Hochschild, G., The Structure of Lie Groups (Holden-Day, Inc., San Francisco, 1965).Google Scholar
5.Heloason, S., Differential Geometry Lie Groups and Symmetric Spaces (Academic Press, New York, 1978).Google Scholar
6.Iwasawa, K., On some types of topological groups, Ann. of Math. 50 (1949), 507–558.CrossRefGoogle Scholar
7.Lee, D. H. and Wu, T. S., On the group of automorphisms of a finite-dimensional topological group, Michigan Math. J. 15 (1968), 321–324.CrossRefGoogle Scholar
8.Mongomery, D. and Zippin, L., Topological Transformation Groups (Interscience Tracts in Pure and Applied Math., Second Printing, New York, 1964).Google Scholar
9.Gleason, A. and Palais, R., On a class of transformation groups, Amer. J. Math. 799 (1957), 631–648.CrossRefGoogle Scholar
10.Moskowitz, M., Homological algebra in locally compact abelian groups, Trans. Amer. Math. Soc. 127 (1967), 361–404.CrossRefGoogle Scholar
11.Peter, J. and Sund, T., Automorphisms of locally compact groups, Pacific J. Math. 76 (1978), 143–156.CrossRefGoogle Scholar
12.Wu, T. S., Closure of Lie subgroups and almost periodic groups, Bull. Inst. Math. Acad. Sinica 14 (1986), 325–347.Google Scholar