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Equidimensional immersions of locally compact groups

Published online by Cambridge University Press:  24 October 2008

K. H. Hofmann ,
T. S. Wu  and
J. S. Yang
K. H. Hofmann
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, D–6100 Darmstadt, WestGermany
T. S. Wu
Affiliation:
Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A.
J. S. Yang
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
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Extract

Dense immersions occur frequently in Lie group theory. Suppose that exp: g → G denotes the exponential function of a Lie group and a is a Lie subalgebra of g. Then there is a unique Lie group ALie with exponential function exp:a → ALie and an immersion f:ALie→G whose induced morphism L(j) on the Lie algebra level is the inclusion a → g and which has as image an analytic subgroup A of G. The group Ā is a connected Lie group in which A is normal and dense and the corestriction

is a dense immersion. Unless A is closed, in which case f' is an isomorphism of Lie groups, dim a = dim ALie is strictly smaller than dim h = dim H.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 253 - 261
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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