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Surjective Linear Maps Between Root Systems with Zero

Published online by Cambridge University Press:  20 November 2018

D. Ž. Đoković  and
Nguyêñ Q. Thãńg
D. Ž. Đoković
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1
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Abstract

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If R1 and R2 are root systems and there is a linear map which maps R1 ∪{0} onto R2∪{0} we write R1 —> R2. We determine all pairs (R1, R2) of irreducible root systems such that R1 —> R2.

Keywords

17B2017B25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 25 - 34
Copyright
Copyright © Canadian Mathematical Society 1995

References

[B] Borel, A., Linear algebraic groups, Graduate Texts in Math., Second edition, New York, 1991.Google Scholar
[Bo] Bourbaki, N., Groupes et algèbres de Lie, Chapitres IV—VI, Hermann, Paris, 1968.Google Scholar
[BS] Burris, S. and Sankappanavar, H. P., A course in universal algebra, Springer, New York, 1981.Google Scholar
[OV] Onishchik, A. L. and Vinberg, E. B., Lie groups and algebraic groups, Springer, New York, 1990.Google Scholar
[Se] Selbach, M., Klassifikationstheorie der halbeinfacher algebraischer Gruppen, Bonner Math. Schriften 83(1976).Google Scholar
[St] Steinberg, R., Lectures on Chevalley groups, Yale University, 1967.Google Scholar
[Ti] Tits, J., Classification of algebraic semisimple groups, Proc. Sympos. Pure Math. IX(1966), 32–62.Google Scholar
[Wa] Warner, G., Harmonic analysis on semisimple Lie groups, 1, Springer, New York, 1972.Google Scholar