By Jean-Pierre Serre
Those notes are a checklist of a path given in Algiers from lOth to twenty first could, 1965. Their contents are as follows. the 1st chapters are a precis, with out proofs, of the overall houses of nilpotent, solvable, and semisimple Lie algebras. those are famous effects, for which the reader can seek advice from, for instance, bankruptcy I of Bourbaki or my Harvard notes. the idea of advanced semisimple algebras occupies Chapters III and IV. The proofs of the most theorems are primarily whole; although, i've got additionally came across it worthy to say a few complementary effects with no facts. those are indicated via an asterisk, and the proofs are available in Bourbaki, Groupes et Algebres de Lie, Paris, Hermann, 1960-1975, Chapters IV-VIII. a last bankruptcy exhibits, with no facts, tips to go from Lie algebras to Lie teams (complex-and additionally compact). it's only an creation, aimed toward guiding the reader in the direction of the topology of Lie teams and the idea of algebraic teams. i'm satisfied to thank MM. Pierre Gigord and Daniel Lehmann, who wrote up a primary draft of those notes, and in addition Mlle. Franr,:oise Pecha who used to be chargeable for the typing of the manuscript.
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