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Complex Semisimple Lie Algebras

  • Book
  • © 1987

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Authors:
  1. Jean-Pierre Serre

    1. Collège de France, Paris Cedex 05, France

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-ix
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  2. Nilpotent Lie Algebras and Solvable Lie Algebras

    • Jean-Pierre Serre
    Pages 1-4

  3. Semisimple Lie Algebras (General Theorems)

    • Jean-Pierre Serre
    Pages 5-9

  4. Cartan Subalgebras

    • Jean-Pierre Serre
    Pages 10-16

  5. The Algebra sl2 and Its Representations

    • Jean-Pierre Serre
    Pages 17-23

  6. Root Systems

    • Jean-Pierre Serre
    Pages 24-42

  7. Structure of Semisimple Lie Algebras

    • Jean-Pierre Serre
    Pages 43-55

  8. Linear Representations of Semisimple Lie Algebras

    • Jean-Pierre Serre
    Pages 56-65

  9. Complex Groups and Compact Groups

    • Jean-Pierre Serre
    Pages 66-71

  10. Back Matter

    Pages 71-74
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Keywords

About this book

These notes are a record of a course given in Algiers from lOth to 21st May, 1965. Their contents are as follows. The first two chapters are a summary, without proofs, of the general properties of nilpotent, solvable, and semisimple Lie algebras. These are well-known results, for which the reader can refer to, for example, Chapter I of Bourbaki or my Harvard notes. The theory of complex semisimple algebras occupies Chapters III and IV. The proofs of the main theorems are essentially complete; however, I have also found it useful to mention some complementary results without proof. These are indicated by an asterisk, and the proofs can be found in Bourbaki, Groupes et Algebres de Lie, Paris, Hermann, 1960-1975, Chapters IV-VIII. A final chapter shows, without proof, how to pass from Lie algebras to Lie groups (complex-and also compact). It is just an introduction, aimed at guiding the reader towards the topology of Lie groups and the theory of algebraic groups. I am happy to thank MM. Pierre Gigord and Daniel Lehmann, who wrote up a first draft of these notes, and also Mlle. Franr,:oise Pecha who was responsible for the typing of the manuscript.

Authors and Affiliations

  • Collège de France, Paris Cedex 05, France

    Jean-Pierre Serre

Bibliographic Information

  • Book Title: Complex Semisimple Lie Algebras

  • Authors: Jean-Pierre Serre

  • DOI: https://doi.org/10.1007/978-1-4757-3910-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1987

  • Softcover ISBN: 978-0-387-96569-7Published: 23 October 1987

  • eBook ISBN: 978-1-4757-3910-7Published: 14 March 2013

  • Edition Number: 1

  • Number of Pages: IX, 74

  • Topics: Topological Groups, Lie Groups

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