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Proceedings of the American Mathematical Society

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

 

 

Lie groups isomorphic to direct products of unitary groups


Authors: Ivan Vidav and Peter Legiša
Journal: Proc. Amer. Math. Soc. 56 (1976), 363-364
MSC: Primary 22E10
DOI: https://doi.org/10.1090/S0002-9939-1976-0422495-6
MathSciNet review: 0422495
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Abstract: A criterion is given for a compact connected subgroup of Gl$ (n,{\mathbf{C}})$ to be isomorphic to a direct product of unitary groups. It implies that a compact connected subgroup of rank $ n$ in Gl$ (n,{\mathbf{C}})$ is isomorphic to a direct product of unitary groups.


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

  • [1] J. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560
  • [2] C. Chevalley, Theory of Lie groups. Vol. 1, Princeton Math. Ser., vol. 8, Princeton Univ. Press, Princeton, N.J., 1946. MR 7, 412.
  • [3] Ivan Vidav, The group of isometries and the structure of a finite-dimensional Banach space, Linear Algebra and Appl. 14 (1976), no. 3, 227–236. MR 0473865

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DOI: https://doi.org/10.1090/S0002-9939-1976-0422495-6
Article copyright: © Copyright 1976 American Mathematical Society