矩阵群:李群理论基础(英文影印版)

3.3 The Lie Algebras of Some Matrix Groups
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
7.0 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...