On conjugacy classes of elements of finite order in compact or complex semisimple Lie groups
Author:
Dragomir Ž. Djoković
Journal:
Proc. Amer. Math. Soc. 80 (1980), 181-184
MSC:
Primary 20G20; Secondary 22E10
DOI:
https://doi.org/10.1090/S0002-9939-1980-0574532-7
MathSciNet review:
574532
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Abstract | References | Similar Articles | Additional Information
Abstract: If K is a connected compact Lie group with simple Lie algebra and if k is an integer relatively prime to the order of the Weyl group W of K then the number of conjugacy classes of K consisting of elements x satisfying
is given by



- [1] N. Bourbaki, Groupes et algèbres de Lie, Hermann, Paris, 1968, Chapters 4-6. MR 0240238 (39:1590)
- [2] M. Newman, Integral matrices, Academic Press, New York, 1972. MR 0340283 (49:5038)
- [3] L. Solomon, Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), 57-64. MR 0154929 (27:4872)
- [4] T. A. Springer, Regular elements of finite reflection groups, Invent. Math. 25 (1974), 159-198. MR 0354894 (50:7371)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1980-0574532-7
Keywords:
Semisimple complex Lie group,
compact semisimple group,
Weyl group,
conjugacy classes,
orbits,
exponents of the Weyl group
Article copyright:
© Copyright 1980
American Mathematical Society