图书信息
图书目录
Lie 型有限单群中的扩展性（影印版）
暂无简介
作者：
Terence Tao
定价：
135.00元
出版时间：
2023-03-08
ISBN：
978-7-04-059297-9
物料号：
59297-00
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
重点项目：
暂无
版面字数：
500.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
- Chapter 1. Expander graphs: Basic theory
- 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
- Chapter 8. Cayley graphs and the algebra of groups
