群表示论导引（影印版）

样章

作者：

Emmanuel Kowalski

定价：

169.00 元

版面字数：

700.000千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2022年

ISBN：

978-7-04-056978-0

物料号：

56978-00

出版时间：

2022-02-25

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
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