《李代數和代數群(英文)》中所討論的局部李群方法提供了求解非線性方程解析解通用且非常有效的方法，而近似變換群可以提高構造含少量參數的微分方程的技巧。《李代數和代數群(英文)》通俗易懂、敘述清晰，並提供豐富的模型，能幫助讀者輕鬆地逐步深人各種主題。
基本介紹
- 書名：李代數和代數群
- 作者：陶威爾 (Tauvel P.)
- 出版日期：2014年3月1日
- 語種：簡體中文, 英語
- ISBN：9787510070228
- 外文名：Lie Algebras and Algebraic Groups
- 出版社：世界圖書出版公司北京公司
- 頁數：653頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《李代數和代數群(英文)》由世界圖書出版北京公司出版。
作者簡介
作者：（法國）陶威爾（Tauvel P.）
圖書目錄
Results on topological spaces
1.1 Irreducible sets and spaces
1.2 Dimension
1.3 Noetherian spaces
1.4 Constructible sets
1.5 Gluing topological spaces
Rings and modules
2.1 Ideals
2.2 Prime and maximal ideals
2.3 Rings of fractions and localization
2.4 Localizations of modules.
2.5 Radical of an ideal
2.6 Local rings
2.7 Noetherian rings and modules
2.8 Derivations
2.9 Module of differentials
Integral extensions
3.1 Integral dependence
3.2 Integrally closed domains
3.3 Extensions of prime ideals
Factorial rings
4.1 Generalities
4.2 Unique factorization
4.3 Principal ideal domains and Euclidean domains
4.4 Polynomials and factorial rings
4.5 Symmetric polynomials
4.6 Resultant and discriminant.
5 Field extensions 55
5.1 Extensions 55
5.2 Algebraic and transcendental elements 56
5.3 Algebraic extensions 56
5.4 Transcendence basis 58
5.5 Norm and trace 60
5.6 Theorem of the primitive element 62
5.7 Going Down Theorem 64
5.8 Fields and derivations 67
5.9 Conductor 70
Finitely generated algebras 75
6.1 Dimension 75
6.2 Noether's Normalization Theorem 76
6.3 Krull's Principal Ideal Theorem 81
6.4 Maximal ideals 82
6.5 Zariski topology 84
Gradings and filtrations 87
7.1 Graded rings and graded modules 87
7.2 Graded submodules 88
7.3 Applications 90
7.4 Filtrations 91
7.5 Grading associated to a filtration 92
Inductive limits 95
8.1 Generalities 95
8.2 Inductive systems of maps 96
8.3 Inductive systems of magmas， groups and rings 98
8.4 An example ； 100
8.5 Inductive systems of algebras
Sheaves of functions 103
9.1 Sheaves 103
9.2 Morphisms 104
9.3 Sheaf associated to a presheaf
9.4 Gluing 109
9.5 Ringed space 110
10 Jordan decomposition and some basic results on groups
10.1 Jordan decomposition 113
10.2 Generalities on groups 117
10.3 Commutators 118
10.4 Solvable groups 120
10.5 Nilpotent groups 121
10.6 Group actions
10.7 Generalities on representations
10.8 Examples
11 Algebraic sets
11.1 Affine algebraic sets
11.2 Zariski topology
11.3 Regular functions
11.4 Morphisms
11.5 Examples of morphisms
11.6 Abstract algebraic sets
11.7 Principal open subsets
11.8 Products of algebraic sets
12 Prevarieties and varieties
12.1 Structure sheaf
12.2 Algebraic prevarieties
12.3 Morphisms of prevarieties
12.4 Products of prevarieties
12.5 Algebraic varieties
12.6 Gluing
12.7 Rational functions
12.8 Local rings of a variety
13 Projective varieties
13.1 Projective spaces
13.2 Projective spaces and varieties
13.3 Cones and projective varieties
13.4 Complete varieties
13.5 Products
13.6 Grassmannian variety
14 Dimension
14.1 Dimension of varieties
14.2 Dimension and the number of equations
14.3 System of parameters
14.4 Counterexamples
15 Morphisms and dimertsion
15.1 Criterion of allineness
15.2 Afline morphisms
15.3 Finite morphisms
15.4 Factorization and applications
15.5 Dimension of fibres of a morphism
15.6 An example
……
References
List of notations
Index
1.1 Irreducible sets and spaces
1.2 Dimension
1.3 Noetherian spaces
1.4 Constructible sets
1.5 Gluing topological spaces
Rings and modules
2.1 Ideals
2.2 Prime and maximal ideals
2.3 Rings of fractions and localization
2.4 Localizations of modules.
2.5 Radical of an ideal
2.6 Local rings
2.7 Noetherian rings and modules
2.8 Derivations
2.9 Module of differentials
Integral extensions
3.1 Integral dependence
3.2 Integrally closed domains
3.3 Extensions of prime ideals
Factorial rings
4.1 Generalities
4.2 Unique factorization
4.3 Principal ideal domains and Euclidean domains
4.4 Polynomials and factorial rings
4.5 Symmetric polynomials
4.6 Resultant and discriminant.
5 Field extensions 55
5.1 Extensions 55
5.2 Algebraic and transcendental elements 56
5.3 Algebraic extensions 56
5.4 Transcendence basis 58
5.5 Norm and trace 60
5.6 Theorem of the primitive element 62
5.7 Going Down Theorem 64
5.8 Fields and derivations 67
5.9 Conductor 70
Finitely generated algebras 75
6.1 Dimension 75
6.2 Noether's Normalization Theorem 76
6.3 Krull's Principal Ideal Theorem 81
6.4 Maximal ideals 82
6.5 Zariski topology 84
Gradings and filtrations 87
7.1 Graded rings and graded modules 87
7.2 Graded submodules 88
7.3 Applications 90
7.4 Filtrations 91
7.5 Grading associated to a filtration 92
Inductive limits 95
8.1 Generalities 95
8.2 Inductive systems of maps 96
8.3 Inductive systems of magmas， groups and rings 98
8.4 An example ； 100
8.5 Inductive systems of algebras
Sheaves of functions 103
9.1 Sheaves 103
9.2 Morphisms 104
9.3 Sheaf associated to a presheaf
9.4 Gluing 109
9.5 Ringed space 110
10 Jordan decomposition and some basic results on groups
10.1 Jordan decomposition 113
10.2 Generalities on groups 117
10.3 Commutators 118
10.4 Solvable groups 120
10.5 Nilpotent groups 121
10.6 Group actions
10.7 Generalities on representations
10.8 Examples
11 Algebraic sets
11.1 Affine algebraic sets
11.2 Zariski topology
11.3 Regular functions
11.4 Morphisms
11.5 Examples of morphisms
11.6 Abstract algebraic sets
11.7 Principal open subsets
11.8 Products of algebraic sets
12 Prevarieties and varieties
12.1 Structure sheaf
12.2 Algebraic prevarieties
12.3 Morphisms of prevarieties
12.4 Products of prevarieties
12.5 Algebraic varieties
12.6 Gluing
12.7 Rational functions
12.8 Local rings of a variety
13 Projective varieties
13.1 Projective spaces
13.2 Projective spaces and varieties
13.3 Cones and projective varieties
13.4 Complete varieties
13.5 Products
13.6 Grassmannian variety
14 Dimension
14.1 Dimension of varieties
14.2 Dimension and the number of equations
14.3 System of parameters
14.4 Counterexamples
15 Morphisms and dimertsion
15.1 Criterion of allineness
15.2 Afline morphisms
15.3 Finite morphisms
15.4 Factorization and applications
15.5 Dimension of fibres of a morphism
15.6 An example
……
References
List of notations
Index
