By Jean-Pierre Serre
Those notes are a list of a path given in Algiers from lOth to twenty first might, 1965. Their contents are as follows. the 1st chapters are a precis, with no proofs, of the final 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 basically whole; notwithstanding, i've got additionally chanced on it beneficial to say a few complementary effects with out evidence. those are indicated through 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 out evidence, tips to move 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 chuffed to thank MM. Pierre Gigord and Daniel Lehmann, who wrote up a primary draft of those notes, and likewise Mlle. Franr,:oise Pecha who used to be chargeable for the typing of the manuscript.
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