新書推薦：
《
叹为观纸 中国古纸的传说与历史
》
售價：HK$
86.9
《
中国历代男子服饰：图解中国男子传统服饰 解密古代男子穿什么 为什么这样穿
》
售價：HK$
107.8
《
经济学的观念：13位经济学巨匠和他们改变世界的思想（一本书领略群星璀璨的百年经济思想史）
》
售價：HK$
85.8
《
别乱穿 找准你的专属色：四季十二型人色彩穿搭图解 四季型人色彩搭配
》
售價：HK$
54.8
《
香气正念：用气味调节情绪与身体的嗅觉疗愈革命
》
售價：HK$
65.8
《
遗失的文明：走进神秘的考古世界
》
售價：HK$
217.8
《
光绪帝传
》
售價：HK$
54.8
《
名士自风流：中国古代隐士传
》
售價：HK$
46.2
|
| 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
