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Complex Semisimple Lie Algebras (Paperback)
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Complex Semisimple Lie Algebras (Paperback)
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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.
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