Author: Serre, Jean-Pierre
Edition #2; Springer Monographs in Mathematics,; Hardback; Book; 6 Figures, Bibliography, Index
83 pages
Published: November 2000
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 3540678271

These notes give the basic theory of semisimple Lie algebras over the complex numbers including the basic classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and representation theory. The theory is illustrated by using the example of Sl n; in particular, the representation theory of Sl 2 is completely worked out. The last chapter discusses the connection between Lie algebras and Lie groups, and is intended to guide the reader towards further study.These notes give the basic theory of semisimple lie algebras over the complex numbers including the basic classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras.