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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lie groups isomorphic to direct products of unitary groups
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by Ivan Vidav and Peter Legiša PDF
Proc. Amer. Math. Soc. 56 (1976), 363-364 Request permission

Abstract:

A criterion is given for a compact connected subgroup of $\text {Gl} (n,{\mathbf {C}})$ to be isomorphic to a direct product of unitary groups. It implies that a compact connected subgroup of rank $n$ in $\text {Gl} (n,{\mathbf {C}})$ is isomorphic to a direct product of unitary groups.
References
  • J. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560
  • C. Chevalley, Theory of Lie groups. Vol. 1, Princeton Math. Ser., vol. 8, Princeton Univ. Press, Princeton, N.J., 1946. MR 7, 412.
  • Ivan Vidav, The group of isometries and the structure of a finite-dimensional Banach space, Linear Algebra Appl. 14 (1976), no. 3, 227–236. MR 473865, DOI 10.1016/0024-3795(76)90069-0
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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