Complex Semisimple Lie Algebras

Jean-Pierre Serre

Complex Semisimple Lie Algebras
Format
Hardback
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Country
Germany
Published
12 December 2000
Pages
75
ISBN
9783540678274

Complex Semisimple Lie Algebras

Jean-Pierre Serre

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These notes, already well known in their original French edition, 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 sln; in particular, the representation theory of sl2 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.

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