新書推薦：
《
风湿免疫科医师效率手册（第3版）
》
售價：HK$
64.9
《
未来已来：2025人文社会科学智能发展蓝皮书
》
售價：HK$
132.0
《
养猫是一件正经事！——我的猫咪养育全攻略
》
售價：HK$
74.8
《
PCB封装与原理图库工程设计
》
售價：HK$
86.9
《
长棍格斗
》
售價：HK$
118.8
《
梵高·笔记（方尖碑）精选梵高传中的金句 以及部分较为少见的梵高素描作品 带有笔记风格 兼具记事本 盖章本 素描本等多种功能
》
售價：HK$
42.9
《
生命 生存 生活：道家人生哲学智慧
》
售價：HK$
130.9
《
货币的社会生命（社会学新知）
》
售價：HK$
162.8
|
| 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
