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[法] 陶威尔(Tauvel P.) 著
出版社: 世界图书出版公司 ISBN:9787510070228 版次:1 商品编码:11551549 包装:平装 外文名称:Lie Algebras and Algebraic Groups 开本:24开 出版时间:2014-03-01 用纸:胶版纸 页数:653 正文语种:英文
The general theory of algebraic groups is studied in chapter8 21 to 28. The relations between Lie algebras and algebraic groups, which are fundamental to us, are established in chapters 23 and 24. Chapter 29 present8 applications of these relations to tackle the systematic study of Lie algebras. The reader will observe that the geometrical aspects have an important part in this study.In particular, the orbits of points under the action of an algebraic group plays a central role.
1.1 Irreducible sets and spaces
1.2 Dimension
1.3 Noetherian spaces
1.4 Constructible sets
1.5 Gluing topological spaces
2 Ring8 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
3 Integral extensions
3.1 Integral dependence
3.2 Integrally closed domains
3.3 Extensions of prime ideals
4 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
5.1 Extensions
5.2 Algebraic and transcendental elements
5.3 Algebraic extensions
5.4 Transcendence basis
5.5 Norm and trace
5.6 Theorem of the primitive element
5.7 Going Down Theorem
5.8 Fields and derivations
5.9 Conductor
6 Finitely generated algebras
6.1 Dimension
6.2 Noether's Normalization Theorem
6.3 Krull's Principal Ideal Theorem*
6.4 Maximal ideals
6.5 Zariski topology
7 Gradings and filtrations
7.1 Graded rings and graded modules
7.2 Graded submodules
7.3 Applications
7.4 Filtrations
7.5 Grading associated to a filtration
8 Inductive limits
8.1 Generalities
8.2 Inductive systems of maps
8.3 Inductive systems of magmas, groups and rings
8.4 An example
8.5 Inductive systems of algebras
9 Sheaves of functions
9.1 Sheaves
9.2 Morphisms
9.3 Sheaf associated to a presheaf
9.4 Gluing
9.5 Ringed space
10 Jordan decomposition and some basic results on groups
10.1 Jordan decomposition
10.2 Generalities on groups
10.3 Commutators
10.4 Solvable groups
10.5 Nilpotent groups
……
11 Algebraic sets
12 Prevarieties and varieties
13 Projective varieties
14 Dimension
15 Morphisms and dimension
16 Tangent 8paces
17 Normal varieties
18 Root systems
19 Lie algebras
20 Semisimple and reductive Lie algebras
21 Algebraic groups
22 Affine algebraic groups
23 Lie algebra of an algebraic group
24 Correspondence between groups and Lie algebras
25 Homogeneous space8 and quotients
38 Semisimple symmetric Lie algebras
39 Sheets of Lie algebras,
40 Index and linear forms
References
List of notations
Index
经典数学丛书(影印版):李代数和代数群 [Lie Algebras and Algebraic Groups] 电子书 下载 mobi epub pdf txt
经典数学丛书(影印版):李代数和代数群 [Lie Algebras and Algebraic Groups]-so88
经典数学丛书(影印版):李代数和代数群 [Lie Algebras and Algebraic Groups] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[法] 陶威尔(Tauvel P.) 著
出版社: 世界图书出版公司 ISBN:9787510070228 版次:1 商品编码:11551549 包装:平装 外文名称:Lie Algebras and Algebraic Groups 开本:24开 出版时间:2014-03-01 用纸:胶版纸 页数:653 正文语种:英文
内容简介
The theory of groups and Lie algebras is interesting for many reasons. In the mathematical viewpoint, it employs at the same time algebra, analysis and geometry. On the other hand, it intervenes in other areas of science, in particular in different branches of physic8 and chemistry. It is an active domain of current research.The general theory of algebraic groups is studied in chapter8 21 to 28. The relations between Lie algebras and algebraic groups, which are fundamental to us, are established in chapters 23 and 24. Chapter 29 present8 applications of these relations to tackle the systematic study of Lie algebras. The reader will observe that the geometrical aspects have an important part in this study.In particular, the orbits of points under the action of an algebraic group plays a central role.
内页插图
目录
1 Results on topological spaces1.1 Irreducible sets and spaces
1.2 Dimension
1.3 Noetherian spaces
1.4 Constructible sets
1.5 Gluing topological spaces
2 Ring8 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
3 Integral extensions
3.1 Integral dependence
3.2 Integrally closed domains
3.3 Extensions of prime ideals
4 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
5.1 Extensions
5.2 Algebraic and transcendental elements
5.3 Algebraic extensions
5.4 Transcendence basis
5.5 Norm and trace
5.6 Theorem of the primitive element
5.7 Going Down Theorem
5.8 Fields and derivations
5.9 Conductor
6 Finitely generated algebras
6.1 Dimension
6.2 Noether's Normalization Theorem
6.3 Krull's Principal Ideal Theorem*
6.4 Maximal ideals
6.5 Zariski topology
7 Gradings and filtrations
7.1 Graded rings and graded modules
7.2 Graded submodules
7.3 Applications
7.4 Filtrations
7.5 Grading associated to a filtration
8 Inductive limits
8.1 Generalities
8.2 Inductive systems of maps
8.3 Inductive systems of magmas, groups and rings
8.4 An example
8.5 Inductive systems of algebras
9 Sheaves of functions
9.1 Sheaves
9.2 Morphisms
9.3 Sheaf associated to a presheaf
9.4 Gluing
9.5 Ringed space
10 Jordan decomposition and some basic results on groups
10.1 Jordan decomposition
10.2 Generalities on groups
10.3 Commutators
10.4 Solvable groups
10.5 Nilpotent groups
……
11 Algebraic sets
12 Prevarieties and varieties
13 Projective varieties
14 Dimension
15 Morphisms and dimension
16 Tangent 8paces
17 Normal varieties
18 Root systems
19 Lie algebras
20 Semisimple and reductive Lie algebras
21 Algebraic groups
22 Affine algebraic groups
23 Lie algebra of an algebraic group
24 Correspondence between groups and Lie algebras
25 Homogeneous space8 and quotients
38 Semisimple symmetric Lie algebras
39 Sheets of Lie algebras,
40 Index and linear forms
References
List of notations
Index
前言/序言
经典数学丛书(影印版):李代数和代数群 [Lie Algebras and Algebraic Groups] 电子书 下载 mobi epub pdf txt
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