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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: 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.


References [Enhancements On Off] (What's this?)

  • [1] L. Auslander, Unitary representations of locally compact groups, Lecture Note, Yale University, New Haven, Conn., 1961/62.
  • [2] 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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0263978-6
Keywords: Epimorphisms, category, compact groups, finite-dimensional representations, unitary transformations
Article copyright: © Copyright 1970 American Mathematical Society