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Generators of Chevalley Groups over Z

Published online by Cambridge University Press:  20 November 2018

Bomshik Chang
Bomshik Chang*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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Let be the universal Chevalley group ([1], p. 197) of type over a field K and where Ф is the set of roots of . Let n = {α1, α2, …, an} be a fundamental system of roots of and put

Then we know from [2] (p. 950) that

where h is the Coxeter number of We call an element of conjugate to W a Coxeter element and an element conjugate to M a Kac element.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 2 , 01 April 1986 , pp. 387 - 396
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Carter, R. W., Simple groups of Lie type (John Wiley, New York, 1972).Google Scholar
2. Chang, B., Elements of order Coxeter number + 1 in Chevalley groups, Can. J. Math. 34 (1982), 945–951.Google Scholar
3. Chevalley, C., Classifications des groupes de Lie algébriques, vol. 2 (Secretariat mathématique, Paris, 1958).Google Scholar