新書推薦：
《
史学视角下的跨文化研究（一）： 追踪谱系、轨迹与多样性
》
售價：HK$
104.5
《
历史文本的文化间交织：中国上古历史及其欧洲书写（论衡系列）
》
售價：HK$
118.8
《
1688：第一次现代革命（革命不是新制度推翻旧制度，而是两条现代化道路的殊死斗争！屡获大奖，了解光荣革命可以只看这一本）
》
售價：HK$
217.8
《
东方小熊日本幼儿园思维训练 听力专注力（4册）
》
售價：HK$
88.0
《
粤港澳大湾区世界重要人才中心和创新高地建设
》
售價：HK$
107.8
《
她们登上了太空：第一批NASA女性宇航员成长纪实
》
售價：HK$
107.8
《
当代资本主义日常生活金融化研究
》
售價：HK$
140.8
《
证明的故事：从勾股定理到现代数学
》
售價：HK$
131.8
|
| 內容簡介： |
|
塞潘斯基编著的《紧李群（影印版）》是“国外数学名著系列”之一，内容包括紧李群、群表示论、调和分析、李代数、阿贝尔李子群等。可供高等院校数学专业研究生、数学类科研人员学习参考。
|
| 目錄：
|
Preface
1 Compact Lie Groups
1.1 Basic Notions
1.1.1 Manifolds
1.1.2 Lie Groups
1.1.3 Lie Subgroups and Homomorphisms
1.1.4 Compact Classical Lie Groups
1.1.5 Exercises
1.2 Basic Topology
1.2.1 Connectedness
1.2.2 Simply Connected Cover
1.2.3 Exercises
1.3 The Double Cover of SOn
1.3.1 Clifford Algebras
1.3.2 SpinnIR and Pin
1.3.3 Exercises
1.4 Integration
1.4.1 Volume Forms
1.4.2 Invafiant Integration
1.4.3 Fubini''s Theorem
1.4.4 Exercises
2 Representations
2.1 Basic Notions
2.1.1 Definitions
2.1.2 Examples
2.1.3 Exercises
2.2 Operations on Representations
2.2.1 Constructing New Representations
2.2.2 Irreducibility and Schur''s Lemma
2.2.3 Unitarity
2.2.4 Canonical Decomposition
2.2.5 Exercises
2.3 Examples of Irreducibility
2.3.1 SU2 and VnC2
2.3.2 SOn and Harmonic Polynomials
2.3.3 Spin and Half-Spin Representations
2.3.4 Exercises
3 Harmonic Analysis
3.1 Matrix Coefficients
3.1.1 Schur Orthogonality
3.1.2 Characters
3.1.3 Exercises
3.2 Infinite-Dimensional Representations
3.2.1 Basic Definitions and Schur''s Lemma
3.2.2 G-Finite Vectors
3.2.3 Canonical Decomposition
3.2.4 Exercises
3.3 The Peter-Weyl Theorem
3.3.1 The Left and Right Regular Representation
3.3.2 Main Result
3.3.3 Applications
3.3.4 Exercises
3.4 Fourier Theory
3.4.1 Convolution
3.4.2 Plancherel Theorem
3.4.3 Projection Operators and More General Spaces
3.4.4 Exercises
4 Lie Algebras
4.1 Basic Definitions
4.1.1 Lie Algebras of Linear Lie Groups
4.1.2 Exponential Map
4.1.3 Lie Algebras for the Compact Classical Lie Groups
4.1.4 Exercises
4.2 Further Constructions
4.2.1 Lie Algebra Homomorphisms
4.2.2 Lie Subgroups and Subalgebras
4.2.3 Covering Homomorphisms
4.2.4 Exercises
5 Abelian Lie Subgroups and Structure
5.1 Abelian Subgroups and Subalgebras
5.1.1 Maximal Tori and Caftan Subalgebras
5.1.2 Examples
5.1.3 Conjugacy of Cartan Subalgehras
5.1.4 Maximal Torus Theorem
5.1.5 Exercises
5.2 Structure
5.2.1 Exponential Map Revisited
5.2.2 Lie Algebra Structure
5.2.3 Commutator Theorem
5.2.4 Compact Lie Group Structure
5.2.5 Exercises
6 Roots and Associated Structures
6.1 Root Theory
6.1.1 Representations of Lie Algebras
6.1.2 Complexification of Lie Algebras
6.1.3 Weights
6.1.4 Roots
6.1.5 Compact Classical Lie Group Examples
6.1.6 Exercises
6.2 The Standard s[2, C Triple
6.2.1 Cartan Involution
6.2.2 Killing Form
6.2.3 The Standard sl2, C and su2 Triples
6.2.4 Exercises
6.3 Lattices
6.3.1 Definitions
6.3.2 Relations
6.3.3 Center and Fundamental Group
6.3.4 Exercises
6.4 Weyl Group
6.4.1 Group Picture
6.4.2 Classical Examples
6.4.3 Simple Roots and Weyl Chambers
6.4.4 The Weyl Group as a Reflection Group
6.4.5 Exercises
7 Highest Weight Theory
7.1 Highest Weights
7.1.1 Exercises
7.2 Weyl Integration Formula
7.2.1 Regular Elements
7.2.2 Main Theorem
7.2.3 Exercises
7.3 Weyl Character Formula
7.3.1 Machinery
7.3.2 Main Theorem
7.3.3 Weyl Denominator Formula
7.3.4 Weyl Dimension Formula
7.3.5 Highest Weight Classification
7.3.6 Fundamental Group
7.3.7 Exercises
7.4 Borel-Weil Theorem
7.4.1 Induced Representations
7.4.2 Complex Structure on GT
7.4.3 Holomorphic Functions
7.4.4 Main Theorem
7.4.5 Exercises
References
Index
|
|
購物車/收銀台(0) | 在線留言板
| 付款方式
| 運費計算
| 聯絡我們
| 幫助中心 |
加入書簽
HOME
新書上架
