作者：Jean-Pierre Serre[著]
页数：10,170页
出版社：世界图书出版公司
出版日期：2008
ISBN：9787506292597
电子书格式：pdf/epub/txt
内容简介
本书是一部非常经典的介绍有限群线性表示的教程，原版曾多次修订重印，作者是当今法国最突出的数学家之一，他对理论数学有全面的了解，尤以著述清晰、明了闻名。本书是他写的为数不多的教科书之一，原文是法文(1971年版)，后出了德译本和英译本。本书是英译本的重印本，篇幅不大，但深入浅出地介绍了有限群的线性表示，并给出了在量子化学等方面的应用，便于广大数学、物理、化学工作者初学时阅读和参考。
目次：第一部分：表示和特征：线性表示概念；特征理论；子群、乘积、导出表示；紧群；例子；第二部分：特征零上的表示：群代数；导出表示；导出表示例子；Artin定理；Brauer定理；rauer定理的应用；合理性问题；合理性问题例子；第三部分：Brauer理论导论：群Rk(G),RK(G),Pk(G)；三角同态；定理；若干证明；模特征标；
读者对象：本书适用于数学专业的学生、老师以及相关专业的科研人员。
作者简介
J-P Serre，法国数学家，主要贡献的领域是拓扑学、代数几何与数论，曾获得许多数学奖项，包括1954年的费尔兹奖与2003年的阿贝尔奖。
目录
Part Ⅰ Representations and Characters
1 Generalities on linear representations
1.1 Definitions
1.2 Basic examples
1.3 Subrepresentations
1.4 Irreducible representations
1.5 Tensor product of two representations
1.6 Symmetiic square and alternating square
2 Character theory
2.1 The character of a representation
2.2 Schur’s lemma; basic applications
2.3 Orthogonality’reiations for characters
2.4 Decomposition of the regular representation
2.5 Number of irreducible representations
2.6 Canonical decomposition of a representation
2.7 Explicit decomposition of a representation
3 Subgroups, products, induced representations
3.1 Abelian subgroups
3.2 Product of two groups
3.3 Induced representations
4 Compact groups
4.1 Compact groups
4.2 lnvariant measure on a compact group
4.3 Linear representations of compact groups
5 Examples
5.1 The cyclic Group Cn
5.2 The group C
5.3 The dihedral group D
5.4 The group Dn
5.5 The group D
5.6 The group D
5.7 The alternating group
5.8 The symmetric group
5.9 The group of the cube
Bibliography: Part I
Part Ⅱ Representations in Characteristic Zero
6 The group algebra
6,1 Representations and modules
6.2 Decomposition of C[G]
6.3 The center of C[G]
6.4 Basic properties of integers
6.5 lntegrality properties of characters. Applications
7 Induced representations; Mackey’s criterion
7.1 Induction
7.2 The character of an induced representation; the reciprocity formula
7.3 Restriction to subgroups
7.4 Mackey’s irreducibility criterion
8 Examples of induced representations
8.1 Normal subgroups; applications to the degrees of the irreducible representations
8.2 Semidirect products by an abelian group
8.3 A review of some classes of finite groups
8.4 Sylow’s theorem
8.5 Linear representations of supersolvable groups
9 Artin’s theorem
9.1 The ring R(G)
9,2 Statement of Artin’s theorem
9.3 First proof
9.4 Second proof of (i) (ii)
10 A theorem of Brauer
10.1 p-regular elements;p-elementary subgroups
10.2 Induced characters arising from p-elementary subgroups
10.3 Construction of characters
10.4 Proof of theorems 18 and 18′
10,5 Brauer’s theorem
……
part Ⅲ Introduction to Brauer Theory
Appendix
Bibliography:Part Ⅲ
Index of notation
Index of terminology
1 Generalities on linear representations
1.1 Definitions
1.2 Basic examples
1.3 Subrepresentations
1.4 Irreducible representations
1.5 Tensor product of two representations
1.6 Symmetiic square and alternating square
2 Character theory
2.1 The character of a representation
2.2 Schur’s lemma; basic applications
2.3 Orthogonality’reiations for characters
2.4 Decomposition of the regular representation
2.5 Number of irreducible representations
2.6 Canonical decomposition of a representation
2.7 Explicit decomposition of a representation
3 Subgroups, products, induced representations
3.1 Abelian subgroups
3.2 Product of two groups
3.3 Induced representations
4 Compact groups
4.1 Compact groups
4.2 lnvariant measure on a compact group
4.3 Linear representations of compact groups
5 Examples
5.1 The cyclic Group Cn
5.2 The group C
5.3 The dihedral group D
5.4 The group Dn
5.5 The group D
5.6 The group D
5.7 The alternating group
5.8 The symmetric group
5.9 The group of the cube
Bibliography: Part I
Part Ⅱ Representations in Characteristic Zero
6 The group algebra
6,1 Representations and modules
6.2 Decomposition of C[G]
6.3 The center of C[G]
6.4 Basic properties of integers
6.5 lntegrality properties of characters. Applications
7 Induced representations; Mackey’s criterion
7.1 Induction
7.2 The character of an induced representation; the reciprocity formula
7.3 Restriction to subgroups
7.4 Mackey’s irreducibility criterion
8 Examples of induced representations
8.1 Normal subgroups; applications to the degrees of the irreducible representations
8.2 Semidirect products by an abelian group
8.3 A review of some classes of finite groups
8.4 Sylow’s theorem
8.5 Linear representations of supersolvable groups
9 Artin’s theorem
9.1 The ring R(G)
9,2 Statement of Artin’s theorem
9.3 First proof
9.4 Second proof of (i) (ii)
10 A theorem of Brauer
10.1 p-regular elements;p-elementary subgroups
10.2 Induced characters arising from p-elementary subgroups
10.3 Construction of characters
10.4 Proof of theorems 18 and 18′
10,5 Brauer’s theorem
……
part Ⅲ Introduction to Brauer Theory
Appendix
Bibliography:Part Ⅲ
Index of notation
Index of terminology
