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Algebraic groups and modular Lie algebras

About this Title

James E. Humphreys

Publication: Memoirs of the American Mathematical Society
Publication Year 1967: Number 71
ISBNs: 978-0-8218-1271-6 (print); 978-1-4704-0019-4 (online)
MathSciNet review: 0217075

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Table of Contents


  • 1. Introduction
  • 2. Roots of a semisimple group
  • 3. Cartan decomposition of $L(G)$
  • 4. Groups and algebras of rank two
  • 5. The Lie algebra of a semisimple group
  • 6. The induced adjoint representation
  • 7. Isogenies
  • 8. Chevalley’s theorem
  • 9. Groups of type PA
  • 10. Ideals of $L(G)$. Applications
  • 11. Reductive groups
  • 12. Solvable groups: Preliminaries
  • 13. Maximal tori
  • 14. Borel subgroups
  • 15. Cartan subgroups
  • 16. A conservation theorem
  • 17. Algebraic Lie algebras
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