《Springer大學數學圖書·矩陣群：李群理論基礎》是一本(美國)貝克(Andrew Baker)）編制，由清華大學出版社在2009年11月1日出版的書籍。
基本介紹
- 書名：Springer大學數學圖書·矩陣群：李群理論基礎
- 又名：Matrix Groups: An Introduction to Lie Group Theory
- 作者：(美國)貝克(Andrew Baker)
- ISBN：9787302214847
- 頁數：330頁
- 出版社：清華大學出版社
- 出版時間：2009年11月1日
- 裝幀：平裝
- 開本：16
- 叢書名：Springer 大學數學圖書
- 語言：英語
- 尺寸：24.4 x 17.2 x 1.8 cm
- 重量：581 g
內容簡介,目錄,
內容簡介
《矩陣群:李群理論基礎》講述李群和李代數基礎理論，內容先進，講述方法科學，易於掌握和使用。書中有大量例題和習題（附答案或提示），便於閱讀。適合用作大學數學系和物理系高年級本科生選修課教材、研究生課程教材或參考書。
目錄
Part Ⅰ. Basic Ideas and Examples
1. Real and Complex Matrix Groups
1.1 Groups of Matrices
1.2 Groups of Matrices as Metric Spaces
1.3 Compactness
1.4 Matrix Groups
1.5 Some Important Examples
1.6 Complex Matrices as Real Matrices
1.7 Continuous Homomorphisms of Matrix Groups
1.8 Matrix Groups for Normed Vector Spaces
1.0 Continuous Group Actions
2. Exponentials, Differential Equations and One-parameter Subgroups
2.1 The Matrix Exponential and Logarithm
2.2 Calculating Exponentials and Jordan Form
2.3 Differential Equations in Matrices
2.4 One-parameter Subgroups in Matrix Groups
2.5 One-parameter Subgroups and Differential Equations
3. Tangent Spaces and Lie Algebras
3.1 LieAlgebras.
3.2 Curves, Tangent Spaces and Lie Algebras
3.4 Some Observations on the Exponential Function of a Matrix Group
3.5 SO(3) and SU(2)
3.6 The Complexification of a Real Lie Algebra
4. Algebras, Quaternions and Quaternionic Symplectic Groups
4.1 Algebras
4.2 Real and Complex Normed Algebras
4.3 Linear Algebra over a Division Algebra
4.4 The Quaternions
4.5 Quaternionic Matrix Groups
4.6 Automorphism Groups of Algebras
5. Clifford Algebras and Spinor Groups
5.1 Real Clifford Algebras
5.2 Clifford Groups
5.3 Pinor and Spinor Groups
5.4 The Centres of Spinor Groups
5.5 Finite Subgroups of Spinor Groups
6. Lorentz Groups
6.1 Lorentz Groups
6.2 A Principal Axis Theorem for Lorentz Groups
6.3 SL2(C) and the Lorentz Group Lor(3, 1)
Part Ⅱ. Matrix Groups as Lie Groups
7. Lie Groups
7.1 Smooth Manifolds
7.2 Tangent Spaces and Derivatives
7.3 Lie Groups
7.4 Some Examples of Lie Groups
7.5 Some Useful Formulae in Matrix Groups
7.6 Matrix Groups are Lie Groups
7.7 Not All Lie Groups are Matrix Groups
8. Homogeneous Spaces
8.1 Homogeneous Spaces as Manifolds
8.2 Homogeneous Spaces as Orbits
8.3 Projective Spaces
8.4 Grassmannians
8.5 The Gram-Schmidt Process
8.6 Reduced Echelon Form
8.7 Real Inner Products
8.8 Symplectic Forms
9. Connectivity of Matrix Groups
9.1 Connectivity of Manifolds
9.2 Examples of Path Connected Matrix Groups
9.3 The Path Components of a Lie Group
9.4 Another Connectivity Result
Part Ⅲ. Compact Connected Lie Groups and their Classification
10. Maximal Tori in Compact Connected Lie Groups
10.1 Tori
10.2 Maximal Tori in Compact Lie Groups
10.3 The Normaliser and Weyl Group of a Maximal Torus
10.4 The Centre of a Compact Connected Lie Group
11. Semi-simple Factorisation
11.1 An Invariant Inner Product
11.2 The Centre and its Lie Algebra
11.3 Lie Ideals and the Adjoint Action
11.4 Semi-simple Decompositions
11.5 Structure of the Adjoint Representation
12. Roots Systems, Weyl Groups and Dynkin Diagrams
12.1 Inner Products and Duality
12.2 Roots systems and their Weyl groups
12.3 Some Examples of Root Systems
12.4 The Dynkin Diagram of a Root System
12.5 Irreducible Dynkin Diagrams
12.6 From Root Systems to Lie Algebras
Hints and Solutions to Selected Exercises
Bibliography
Index
