Lie 型有限单群中的扩展性（影印版）

样章

作者：

Terence Tao

定价：

135.00 元

版面字数：

500千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059297-9

物料号：

59297-00

出版时间：

2023-03-08

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

代数学

暂无

目录
- 前辅文
- Part 1. Expansion in Cayley Graphs
  - Chapter 1. Expander graphs: Basic theory
    - §1.1. Expander graphs
    - §1.2. Connection with edge expansion
    - §1.3. Random walks on expanders
    - §1.4. Random graphs as expanders
  - Chapter 2. Expansion in Cayley graphs, and Kazhdan’s property (T)
    - §2.1. Kazhdan’s property (T)
    - §2.2. Induced representations and property (T)
    - §2.3. The special linear group and property (T)
    - §2.4. A more elementary approach
  - Chapter 3. Quasirandom groups
    - §3.1. Mixing in quasirandom groups
    - §3.2. An algebraic description of quasirandomness
    - §3.3. A weak form of Selberg’s 3/16 theorem
  - Chapter 4. The Balog-Szemer´edi-Gowers lemma, and the Bourgain-Gamburd expansion machine
    - §4.1. The Balog-Szemer´edi-Gowers lemma
    - §4.2. The Bourgain-Gamburd expansion machine
  - Chapter 5. Product theorems, pivot arguments, and the Larsen-Pink nonconcentration inequality
    - §5.1. The sum-product theorem
    - §5.2. Finite subgroups of SL2
    - §5.3. The product theorem in SL2(k)
    - §5.4. The product theorem in SLd(k)
    - §5.5. Proof of the Larsen-Pink inequality
  - Chapter 6. Nonconcentration in subgroups
    - §6.1. Expansion in thin subgroups
    - §6.2. Random generators expand
  - Chapter 7. Sieving and expanders
    - §7.1. Combinatorial sieving
    - §7.2. The strong approximation property
    - §7.3. Sieving in thin groups
- Part 2. Related Articles
  - Chapter 8. Cayley graphs and the algebra of groups
    - §8.1. A Hall-Witt identity for 2-cocycles
  - Chapter 9. The Lang-Weil bound
    - §9.1. The Stepanov-Bombieri proof of the Hasse-Weil bound
    - §9.2. The proof of the Lang-Weil bound
    - §9.3. Lang-Weil with parameters
  - Chapter 10. The spectral theorem and its converses for unbounded self-adjoint operators
    - §10.1. Self-adjointness and resolvents
    - §10.2. Self-adjointness and spectral measure
    - §10.3. Self-adjointness and flows
    - §10.4. Essential self-adjointness of the Laplace-Beltrami operator
  - Chapter 11. Notes on Lie algebras
    - §11.1. Abelian representations
    - §11.2. Engel’s theorem and Lie’s theorem
    - §11.3. Characterising semisimplicity
    - §11.4. Cartan subalgebras
    - §11.5. sl2 representations
    - §11.6. Root spaces
    - §11.7. Classification of root systems
    - §11.8. Chevalley bases
    - §11.9. Casimirs and complete reducibility
  - Chapter 12. Notes on groups of Lie type
    - §12.1. Simple Lie groups over C
    - §12.2. Chevalley groups
    - §12.3. Finite simple groups of Lie type
  - Bibliography
  - Index