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Closure Theorem for Analytic Subgroups of Real Lie Groups

Published online by Cambridge University Press:  20 November 2018

D. Ž. Djoković
D. Ž. Djoković*
Affiliation:
Department of Pure Mathematics, University of WaterlooWaterloo, Ontario, Canada
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Let G be a real Lie group, A a closed subgroup of G and B an analytic subgroup of G. Assume that B normalizes A and that AB is closed in G. Then our main result (Theorem 1) asserts that .

This result generalizes Lemma 2 in the paper [4], G. Hochschild has pointed out to me that the proof of that lemma given in [4] is not complete but that it can be easily completed.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 435 - 439
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Gotô, M., Faithful representations of Lie groups I, Math. Japanicae 1 (1948), 107–119.Google Scholar
2. Gotô, M., Faithful representations of Lie groups II, Nagoya Math. J. 1 (1950), 91–107.Google Scholar
3. Hochschild, G., The structure of Lie groups, San Francisco 1965.Google Scholar
4. Hochschild, G., Complexification of real analytic groups, Trans. Amer. Math. Soc. 125 (1966), 406–413.Google Scholar