紧李群

出版时间：2011-6  出版社：科学出版社  作者：塞潘斯基  页数：198  
Tag标签：无  

内容概要

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。

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

用户评论 (总计4条)

•   这是有关紧李群的专著,非常专业,适合数学专业或理论物理专业研究生阅读!
•   一本很精简的书，也是一本比较新的书。介绍了李群和李代数的一些最基本的知识。总的来说比较贵，性价比不高；但是相对于原版来说，已经很便宜了。世图出版社买这个书的版权也是为了便宜一些。
•   内页印刷字体不怎么清楚，而且字号小了一点！影印版就不能多为读者想一想吗？放大一点不行吗？？
•   表示论侧重於torus理论，正好可以结合GTM 98的紧李群表示论读，互相补充.