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群表示论导引（影印版）

暂无简介

作者：

Emmanuel Kowalski

定价：

169.00 元

出版时间：

2022-02-25

ISBN：

978-7-04-056978-0

物料号：

56978-00

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：

700千字

开本：

特殊

装帧形式：

精装

版次：

1

最新版次
印刷时间：

2022年

目录
- 前辅文
- Chapter 1. Introduction and motivation
  - §1.1. Presentation
  - §1.2. Four motivating statements
  - §1.3. Prerequisites and notation
- Chapter 2. The language of representation theory
  - §2.1. Basic language
  - §2.2. Formalism: changing the space
  - §2.3. Formalism: changing the group
  - §2.4. Formalism: changing the field
  - §2.5. Matrix representations
  - §2.6. Examples
  - §2.7. Some general results
  - §2.8. Some Clifford theory
  - §2.9. Conclusion
- Chapter 3. Variants
  - §3.1. Representations of algebras
  - §3.2. Representations of Lie algebras
  - §3.3. Topological groups
  - §3.4. Unitary representations
- Chapter 4. Linear representations of finite groups
  - §4.1. Maschke’s Theorem
  - §4.2. Applications of Maschke’s Theorem
  - §4.3. Decomposition of representations
  - §4.4. Harmonic analysis on finite groups
  - §4.5. Finite abelian groups
  - §4.6. The character table
  - §4.7. Applications
  - §4.8. Further topics
- Chapter 5. Abstract representation theory of compact groups
  - §5.1. An example: the circle group
  - §5.2. The Haar measure and the regular representation of a locally
- compact group
  - §5.3. The analogue of the group algebra
  - §5.4. The Peter–Weyl Theorem
  - §5.5. Characters and matrix coefficients for compact groups
  - §5.6. Some first examples
- Chapter 6. Applications of representations of compact groups
  - §6.1. Compact Lie groups are matrix groups
  - §6.2. The Frobenius–Schur indicator
  - §6.3. The Larsen alternative
  - §6.4. The hydrogen atom
- Chapter 7. Other groups: a few examples
  - §7.1. Algebraic groups
  - §7.2. Locally compact groups: general remarks
  - §7.3. Locally compact abelian groups
  - §7.4. A non-abelian example: SL2pRq
- Appendix A. Some useful facts
  - §A.1. Algebraic integers
  - §A.2. The spectral theorem
  - §A.3. The Stone–Weierstrass Theorem
- Bibliography
- Index