紧李群

紧李群

(美) 塞潘斯基 (Sepanski,M.R.) , 主编

出版社:科学出版社

年代:2011

定价:65.0

书籍简介:

本书内容包括紧李群、群表示论、调和分析、李代数、阿贝尔李子群等。

书籍目录:

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 SO(n)

1.3.1 Clifford Algebras

1.3.2 Spinn(IR) 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 SU(2) and Vn(C2)

2.3.2 SO(n) 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 sl(2, C) and su(2) 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 G/T

7.4.3 Holomorphic Functions

7.4.4 Main Theorem

7.4.5 Exercises

References

Index

内容摘要:

《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。

书籍规格:

书籍详细信息
书名紧李群站内查询相似图书
丛书名国外数学名著系列
9787030313911
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出版地北京出版单位科学出版社
版次影印本印次1
定价(元)65.0语种英文
尺寸24 × 17装帧精装
页数 202 印数

书籍信息归属:

紧李群是科学出版社于2011.6出版的中图分类号为 O152.5 的主题关于 李群-英文 的书籍。