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Lie 型有限单群中的扩展性(影印版)
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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
ISBN:
978-7-04-059297-9
版面字数:
500.000千字
开本:
16开
全书页数:
暂无
装帧形式:
精装
重点项目:
暂无
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
购买:
样章阅读
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图书目录
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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
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