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商品簡介
本書講述李群和李代數基礎理論，內容先進，講述方法科學，易于掌握和使用。書中有大量例題和習題（附答案或提示），便于閱讀。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。
目次
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.O 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
……
4. Algebras, Quaternions and Quaternionic Symplectic Groups
5. Clifford Algebras and Spinor Groups
6. Lorentz Groups
Part II. Matrix Groups as Lie Groups
7. Lie Groups
8. Homogeneous Spaces
9. Connectivity of Matrix Groups
Part III. Compact Connected Lie Groups and their Classification
10. Maximal Tori in Compact Connected Lie Groups
11. Semi simple Factorisation
12. Roots Systems, Weyl Groups and Dynkin Diagrams
Hints and Solutions to Selected Exercises
Bibliography
Index
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.O 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
……
4. Algebras, Quaternions and Quaternionic Symplectic Groups
5. Clifford Algebras and Spinor Groups
6. Lorentz Groups
Part II. Matrix Groups as Lie Groups
7. Lie Groups
8. Homogeneous Spaces
9. Connectivity of Matrix Groups
Part III. Compact Connected Lie Groups and their Classification
10. Maximal Tori in Compact Connected Lie Groups
11. Semi simple Factorisation
12. Roots Systems, Weyl Groups and Dynkin Diagrams
Hints and Solutions to Selected Exercises
Bibliography
Index
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