Epimorphisms of compact groups are onto
Author:
Detlev Poguntke
Journal:
Proc. Amer. Math. Soc. 26 (1970), 503-504
MSC:
Primary 22.60
DOI:
https://doi.org/10.1090/S0002-9939-1970-0263978-6
MathSciNet review:
0263978
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Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that the epimorphisms in the category of compact groups are surjective. The proof is based on the representation theory of compact groups, especially on the well-known fact, that for a closed proper subgroup $H$ of a compact group $G$ there exists an irreducible representation of $G$ which, when restricted to $H$, contains the unit representation.
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L. Auslander, Unitary representations of locally compact groups, Lecture Note, Yale University, New Haven, Conn., 1961/62.
C. Chevalley, Theory of Lie groups, Princeton Math. Series, vol. 8, Princeton Univ. Press, Princeton, N. J., 1946. MR 7, 412.
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Keywords:
Epimorphisms,
category,
compact groups,
finite-dimensional representations,
unitary transformations
Article copyright:
© Copyright 1970
American Mathematical Society