有限群的綫性錶示 [Linear Representations of Finite Groups] epub pdf mobi txt 電子書 下載 2024

有限群的綫性錶示 [Linear Representations of Finite Groups] epub pdf mobi txt 電子書 下載 2024

☆☆☆☆☆
簡體網頁||繁體網頁



點擊這裡下載

有限群的綫性錶示 [Linear Representations of Finite Groups] epub pdf mobi txt 電子書 下載 2024

类似图書 點擊查看全場最低價

---

內容簡介

　　《有限群的綫性錶示》是一部非常經典的介紹有限群綫性錶示的教程，原版曾多次修訂重印，作者是當今法國最突齣的數學傢之一，他對理論數學有全麵的瞭解，尤以著述清晰、明瞭聞名。《有限群的綫性錶示》是他寫的為數不多的教科書之一，原文是法文(1971年版)，後齣瞭德譯本和英譯本。《有限群的綫性錶示》是英譯本的重印本。它篇幅不大，但深入淺齣的介紹瞭有限群的綫性錶示，並給齣瞭在量子化學等方麵的應用，便於廣大數學、物理、化學工作者初學時閱讀和參考。

內頁插圖

目錄

Part Ⅰ
Representations and Characters
1 Generalities on linear representations
1.1 Definitions
1.2 Basic examples
1.3 Submpmsentations
1.4 Irreducible representations
1.5 Tensor product of two representations
1.6 Symmetric square and alternating square

2 Character theory
2.1 The character of a representation
2.2 Schurs lemma; basic applications
2.3 0rthogonality relations 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
5.2 The group
5.3 The dihedral group
5.4 The group
5.5 The group
5.6 The group
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; Mackeys criterion
7.1 Induction
7.2 The character of an induced representation;
the reciprocity formula
7.3 Restriction to subgroups
7.4 Mackeys irreducibility criterion

8 Examples of induced representations
8. l Normal subgroups; applications to the degrees of the
ineducible representations
8.2 Semidirect products by an ahelian group
8.3 A review of some classes of finite groups
8.4 Syiows theorem
8.5 Linear representations of superselvable groups

9 Artins theorem
9.1 The ring R(G)
9.2 Statement of Artins 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 Brauers theorem

11 Applications of Brauers theorem
11.1 Characterization of characters
11.2 A theorem of Frobenius
11.3 A converse to Brauers theorem
11.4 The spectrum of A R(G)

12 Rationality questions
12.1 The rings RK(G) and RK(G)
12.2 Schur indices
12.3 Realizability over cyclotomic fields
12.4 The rank of RK(G)
12.5 Generalization of Artins theorem
12.6 Generalization of Brauers theorem
12.7 Proof of theorem 28

13 Rationality questions： examples
13. I The field Q
13.2 The field R
Bibliography： Part Ⅱ

Part Ⅲ
Introduction to Brauer Theory
14 The groups RK(G)， R(G)， and Pk(G)
14.1 The rings RK(G) and R，(G)
14.2 The groups Pk(G) and P^(G)
14.3 Structure of Pk(G)
14.4 Structure of PA(G)
14.5 Dualities
14.6 Scalar extensions

15 The cde triangle
15.1 Definition of c： Pk(G) ——Rk(G)
15.2 Definition of d： Rs(G) —— Rk(G)
15.3 Definition of e： Pk(G) —— RK(G)
15.4 Basic properties of the cde triangle
15.5 Example： p-gmups
15.6 Example： p-groups
15.7 Example： products ofp-groups and p-groups

16 Theorems
16.1 Properties of the cde triangle
16.2 Characterization of the image of e
16.3 Characterization of projective A [G ]-modules
by their characters
16.4 Examples of projective A [G ]-modules： irreducible
representations of defect zero

17 Proofs
17. I Change of groups
17.2 Brauers theorem in the modular case
17.3 Proof of theorem 33
17.4 Proof of theorem 35
17.5 Proof of theorem 37
17.6 Proof of theorem 38

18 Modular characters
18.1 The modular character of a representation
18.2 Independence of modular characters
18.3 Reformulations
18.4 A section ford
18.5 Example： Modular characters of the symmetric group
18.6 Example： Modular characters of the alternating group

19 Application to Artin representations
19.1 Artin and Swan representations
19.2 Rationality of the Artin and Swan representations
19.3 An invariant

Appendix
Bibliography： Part Ⅲ
Index of notation
Index of terminology

前言/序言

　　This book consists of three parts， rather different in level and purpose：
　　The first part was originally written for quantum chemists. It describes the correspondence， due to Frobenius， between linear representations and characters. This is a fundamental result， of constant use in mathematics as well as in quantum chemistry or physics. I have tried to give proofs as elementary as possible， using only the definition of a group and the rudiments of linear algebra.The examples (Chapter 5) have been chosen from those useful to chemists.

有限群的綫性錶示 [Linear Representations of Finite Groups] epub pdf mobi txt 電子書 下載 2024

有限群的綫性錶示 [Linear Representations of Finite Groups] 下載 epub mobi pdf txt 電子書

評分☆☆☆☆☆

書很好，也很便宜，做活動時買的，大師之作

評分☆☆☆☆☆

在後來的工作上的影響

評分☆☆☆☆☆

書很不錯，價格閤理，送貨很快啊。

評分☆☆☆☆☆

挺好的，字都看的清楚。

評分☆☆☆☆☆

還有, n維反de Sitter空間和有"洛倫茲"特徵數的(n−1)維共形空間（conformal space）(和有"歐幾裏得"特徵數的共形空間不同，那種和逆幾何相同，對於3維以上情況)有同構的自同構群，但是不同的幾何。再次，在物理中有一些在兩個空間中對偶的模型。更多的細節參看AdS/CFT。

評分☆☆☆☆☆

書很不錯，價格閤理，送貨很快啊。

評分☆☆☆☆☆

不錯的商品，比實體店劃算，送貨方便，下次還來！

評分☆☆☆☆☆

在舉一例，不同麯率半徑的橢圓幾何有同構的自同構群。這其實不能算作一個評價，因為所有這種幾何同構。一般的黎曼幾何在這個綱領所能包括的邊界之外。

評分☆☆☆☆☆

為啥我覺得像盜版書

类似图書 點擊查看全場最低價