By Jean-Pierre Serre
Those notes are a checklist of a path given in Algiers from lOth to twenty first may possibly, 1965. Their contents are as follows. the 1st chapters are a precis, with out proofs, of the final homes 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 basically entire; in spite of the fact that, i've got additionally came across it worthwhile to say a few complementary effects with out evidence. those are indicated by means of an asterisk, and the proofs are available in Bourbaki, Groupes et Algebres de Lie, Paris, Hermann, 1960-1975, Chapters IV-VIII. a last bankruptcy indicates, with out evidence, the way to go from Lie algebras to Lie teams (complex-and additionally compact). it is only an advent, geared 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 was once chargeable for the typing of the manuscript.
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