Serre J.-P. — Complex Semisimple Lie Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Serre J.-P. — Complex Semisimple Lie Algebras

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Название: Complex Semisimple Lie Algebras

Автор: Serre J.-P.

Аннотация:

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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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 74

Добавлена в каталог: 18.04.2008

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Предметный указатель

$A_{1}$ (type...)      26
$A_{2}$ (type...)      26
$A_{n}$ (type...)      39-40 62
$B_{2}$ (type...)      26
$B_{n}$ (type...)      40
$C_{n}$ (type...)      40
$D_{n}$ (type...)      40
$E_{6}, E_{7}, E_{8}$ (types...)      41
$F_{n}$ (type...)      40
$\pi(D)$       2
Base (of a root system)      30
Basis (Weyl)      48—49
Borel subalgebra      47—48
Borel subgroup      68—69
Bruhat decomposition      69
Cartan criterion      4
Cartan matrix      34—35 48
Cartan subalgebra      10
Cartan subgroup      66—67
Cartan — Killing criterion      6
Center (of a Lie algebra)      1
Central (lower ... series)      1
Chevalley normalization      51
Compact form      52
Complexification (of a compact group)      71
Complexification (of a real Lie algebra)      9
Coxeter graph      35—36
Derivation (of a Lie algebra)      7
Derived series (of a Lie algebra)      3
Dynkin diagram      38—39
Engel’s theorems      2—3
Fundamental representations      62
Fundamental weights      62
Highest weight      58—60
Indecomposable module      57
Inner automorphisms of a Lie algebra      7
Inner derivation      7

Invariant bilinear form      6
Inverse root      25
Inverse root system      28
Irreducible representation      8
Irreducible root system      36—37
Killing form      6
Levi decomposition      5
Lie’s theorem      4
Multiplicity (of a weight)      56
Nilpotent element      7
Nilpotent Lie algebra      1—2
Normalizer (of a Lie algebra)      10
Positive root      31—32
Primitive element      18 57
Radical (of a Lie algebra)      5
Rank (of a Lie algebra)      11
Rank (of a root system)      25
Real form      9
Reduced root system      25
Regular element      11
Root (of a semisimple Lie algebra)      43
Root system      25—26 41—42
Semisimple element      7
Semisimple Lie algebra      5
Simple Lie algebra      6
Simple root      30
Simple root system      30
Solvable Lie algebra      3—4
Symmetry      24
System (complex root...)      41-42
System (root...)      25-26
Unitarian trick      8 22—23 70
Weight      43 56
Weyl chamber      34
Weyl formula      64—65
Weyl group      27 47
Weyl relations      48
Weyl’s theorem      8

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