Author | Serre, Jean-Pierre. author |
---|---|

Title | Complex Semisimple Lie Algebras [electronic resource] / by Jean-Pierre Serre |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1987 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-3910-7 |

Descript | IX, 74 p. online resource |

SUMMARY

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

CONTENT

I Nilpotent Lie Algebras and Solvable Lie Algebras -- II Semisimple Lie Algebras (General Theorems) -- III Cartan Subalgebras -- IV The Algebra sl2 and Its Representations -- V Root Systems -- VI Structure of Semisimple Lie Algebras -- VII Linear Representations of Semisimple Lie Algebras -- VIII Complex Groups and Compact Groups

Mathematics
Topological groups
Lie groups
Mathematics
Topological Groups Lie Groups