Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T06:36:21.347Z Has data issue: false hasContentIssue false
  • English
  • Français

Solvable Subgroups and their Lie Algebras in Characteristic p

Published online by Cambridge University Press:  20 November 2018

David J. Winter
David J. Winter*
Affiliation:
University of Michigan, Ann Arbor, Michigan
Rights & Permissions [Opens in a new window]

Extract

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.

1. Introduction. Throughout this paper, G is a connected linear algebraic group over an algebraically closed field whose characteristic is denoted p. For any closed subgroup H of G, denotes the Lie algebra of H and H0 denotes the connected component of the identity of H.

A Borel subalgebra of is the Lie algebra of some Borel subgroup B of G. A maximal torus of is the Lie algebra of some maximal torus T of G. In [4], it is shown that the maximal tori of are the maximal commutative subalgebras of consisting of semisimple elements, and the question was raised in § 14.3 as to whether the set of Borel subalgebras of is the set of maximal triangulable subalgebras of .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 308 - 311
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Borel, A. and Springer, T. A., Rationality properties of linear algebraic groups, Proc. Symp. Pure Math., vol. IX (1966), 26–32.Google Scholar
2. Borel, A. and Springer, T. A., Rationality properties of linear algebraic groups II, Tohoku Math. J. 20 (1968), 443–497.Google Scholar
3. Bourbaki, N., Groupes et algèbres de Lie, Chap. 4, 5, 6, Éléments de Mathématique 34, (Hermann, Paris, 1968).Google Scholar
4. Humphreys, J., Algebraic groups and modular Lie algebras, Memoirs AMS No. 71, AMS, Providence (1967).Google Scholar
5. Humphreys, J., Linear algebraic groups, Graduate Texts in Mathematics 21, (Springer Verlag, New York, 1975).Google Scholar
6. Jacobson, N., Lie algebras, (Interscience, New York, 1962).Google Scholar
7. Winter, D. J., Abstract Lie algebras, (MIT Press, Cambridge, 1972).Google Scholar
8. Winter, D. J., On the toral structure of Lie p-algebras, Acta Math. 193 (1969), 69–81.Google Scholar
9. Winter, D. J., Solvable and nilpotent subalgebras of Lie algebras, Bull. AM. 74 (1968), 754–758.Google Scholar