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Lie 型有限单群中的扩展性(影印版)


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

暂无
  • 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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