《LIE ALGEBRAS AND LIE GROUPS》

作者 编者
出版 SPRINGER-VERLAG
参考页数 168
出版时间 1992（求助前请核对）  目录预览
ISBN号 3540550089;0387550089 — 求助条款
PDF编号 812465468（仅供预览，未存储实际文件）
求助格式 扫描PDF（若分多册发行，每次仅能受理1册）
LIE ALGEBRAS AND LIE GROUPS 1992 PDF电子版封面 3540550089;0387550089

Part Ⅰ-Lie Algebras1

Introduction1

Chapter Ⅰ.Lie Algebras：Definition and Examples2

Chapter Ⅱ.Filtered Groups and Lie Algebras6

1.Formulae on commutators6

2.Filtration on a group7

3.Integral filtrations of a group8

4.Filtrations in GL（n）9

Exercises10

Chapter Ⅲ.Universal Algebra of a Lie Algebra11

1.Definition11

2.Functorial properties12

3.Symmetric algebra of a module12

4.Filtration of U？13

5.Diagonal map16

Exercises17

Chapter Ⅳ.Free Lie Algebras18

1.Free magmas18

2.Free algebra on X18

3.Free Lie algebra on X19

4.Relation with the free associative algebra on X20

5.P.Hall families22

6.Free groups24

7.The Campbell-Hausdorff formula26

8.Explicit formula28

Exercises29

Chapter Ⅴ.Nilpotent and Solvable Lie Algebras31

1.Complements on ？-modules31

2.Nilpotent Lie algebras32

3.Main theorems33

3.The group-theoretic analog of Engel’s theorem35

4.Solvable Lie algebras35

5.Main theorem36

5.The group theoretic analog of Lie’s theorem38

6.Lemmas on endomorphisms40

7.Cartan’s criterion42

Exercises43

Chapter Ⅵ.Semisimple Lie Algebras44

1.The radical44

2.Semisimple Lie algebras44

3.Complete reducibility45

4.Levi’s theorem48

5.Complete reducibility continued50

6.Connection with compact Lie groups over R and C53

Exercises54

Chapter Ⅶ.Representations of s？n56

1.Notations56

2.Weights and primitive elements57

3.Irreducible ？-modules58

4.Determination of the highest weights59

Exercises61

Part Ⅱ-Lie Groups63

Introduction63

Chapter Ⅰ.Complete Fields64

Chapter Ⅱ.Analytic Functions67

“Tournants dangereux”75

Chapter Ⅲ.Analytic Manifolds76

1.Charts and atlases76

2.Definition of analytic manifolds77

3.Topological properties of manifolds77

4.Elementary examples of manifolds78

5.Morphisms78

6.Products and sums79

7.Germs of analytic functions80

8.Tangent and cotangent spaces81

9.Inverse function theorem83

10.Immersions，submersions，and subimmersions83

11.Construction of manifolds：inverse images87

12.Construction of manifolds：quotients92

Exercises95

Appendix 1.A non-regular Hausdorff manifold96

Appendix 2.Structure of p-adic manifolds97

Appendix 3.The transfinite p-adic line101

Chapter Ⅳ.Analytic Groups102

1.Definition of analytic groups102

2.Elementary examples of analytic groups103

3.Group chunks105

4.Prolongation of subgroup chunks106

5.Homogeneous spaces and orbits108

6.Formal groups：definition and elementary examples111

7.Formal groups：formulae113

8.Formal groups over a complete valuation ring116

9.Filtrations on standard groups117

Exercises120

Appendix 1.Maximal compact subgroups of GL（n，k）121

Appendix 2.Some convergence lemmas122

Appendix 3.Applications of §9：“Filtrations on standard groups”124

Chapter Ⅴ.Lie Theory129

1.The Lie algebra of an analytic group chunk129

2.Elementary examples and properties130

3.Linear representations131

4.The convergence of the Campbell-Hausdorff formula136

5.Point distributions141

6.The bialgebra associated to a formal group143

7.The convergence of formal homomorphisms149

8.The third theorem of Lie152

9.Cartan’s theorems155

Exercises157

Appendix.Existence theorem for ordinary differential equations158

Bibliography161

Problem163

Index165

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高度相关资料

LIE GROUPS（1957 PDF版）
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Lie Algebras with Triangular Decompositions（ PDF版）
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LIE GROUPS AND COMPACT GROUPS（1979 PDF版）
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Foundations of differentiable manifolds and Lie groups（1983 PDF版）
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1983 世界图书出版公司; Springer-Verlag
Representations of real reductive Lie groups（1981 PDF版）
Representations of real reductive Lie groups
1981 Birkh user Boston
Modular Lie algebras（1967 PDF版）
Modular Lie algebras
1967 Springer-Verlag
Lie algebras and Lie groups : 1964 lectures given at Harvard University（1992 PDF版）
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1992 Springer-Verlag
Lie algebras and locally compact groups（1971 PDF版）
Lie algebras and locally compact groups
1971 University of Chicago Press
Infinite dimensional Lie algebras Second Edition（1985 PDF版）
Infinite dimensional Lie algebras Second Edition
1985 Cambridge University Press
Basic theory of algebraic groups and Lie algebras（1981 PDF版）
Basic theory of algebraic groups and Lie algebras
1981 Springer-Verlag
Lie groups（1957 PDF版）
Lie groups
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Representations of Compact Lie Groups（1985 PDF版）
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1985 Springer Berlin Heidelberg
INFINITE DIMENSIONAL LIE ALGEBRAS THIRD EDITION（1994 PDF版）
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1994 CAMBRIDGE UNIVERSITY PRESS
LIE GROUPS NO.46（1957 PDF版）
LIE GROUPS NO.46
1957 CAMBRIDGE AT THE UNIVERSITY PRESS
LIE GROUPS ASSOCIATED WITH PSEUDO GROUPS（1962 PDF版）
LIE GROUPS ASSOCIATED WITH PSEUDO GROUPS
1962 DEPT. OF COMMERCE

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