| 《矩阵群:李群理论基础》内容先进，讲述方法科学，有大量例子和习题，并附有习题解答或提示，易于使用。《矩阵群:李群理论基础》在Springer出版社SUMS系列（大学生数学系列）中是内容最深的一册。在我国，《矩阵群:李群理论基础》适合用作大学数学系和物理系高年级本科生选修课教材、研究生课程教材或参考书。李群和李代数理论是现代数学和物理学的重要工具，也是比较深刻和难学的理论。各种矩阵群和矩阵代数是李群和李代数最典型和最重要的例子。从矩阵出发讲述这部分数学知识，既能使学生把握内容实质，又能使学生学会计算和使用，所以这是一本不可多得的好教材，应当鼓励中国的老师用这种方法讲述李群和李代数。就内容而言，《矩阵群:李群理论基础》材料本质上不超出我国大学线性代数、抽象代数和一般拓扑学的教学内容；但是《矩阵群:李群理论基础》所讲述的是李群和李代数基础理论。 |
| 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 |
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