Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T06:03:16.222Z Has data issue: false hasContentIssue false

Surjective Linear Maps Between Root Systems with Zero

Published online by Cambridge University Press:  20 November 2018

D. Ž. Đoković
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
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), 3262.Google Scholar
[Wa] Warner, G., Harmonic analysis on semisimple Lie groups, 1, Springer, New York, 1972.Google Scholar