Complex semisimple Lie algebras

Jean-Pierre Serre ; translated from the French by G.A. Jones

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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  • 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.

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書名 Complex semisimple Lie algebras
著作者等 Jones, Gareth A
Serre, Jean Pierre
Jones Glen
Serre Jean-Pierre
書名別名 Algèbres de Lie semi-simples complexes
出版元 Springer
刊行年月 c1987
ページ数 ix, 74 p.
大きさ 24 cm
ISBN 3540965696
NCID BA01301902
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言語 英語
原文言語 フランス語
出版国 アメリカ合衆国