有限群的线性表示

图书标准信息

• 作者 [法]赛尔 著
• 出版社 世界图书出版公司
• 出版时间 2008-10
• 版次 1
• ISBN 9787506292597
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 170页
• 正文语种 英语

【内容简介】

　　《有限群的线性表示》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。《有限群的线性表示》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。《有限群的线性表示》是英译本的重印本。它篇幅不大，但深入浅出的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。

【目录】

PartⅠ
RepresentationsandCharacters
1Generalitiesonlinearrepresentations
1.1Definitions
1.2Basicexamples
1.3Submpmsentations
1.4Irreduciblerepresentations
1.5Tensorproductoftworepresentations
1.6Symmetricsquareandalternatingsquare

2Charactertheory
2.1Thecharacterofarepresentation
2.2Schurslemma;basicapplications
2.30rthogonalityrelationsforcharacters
2.4Decompositionoftheregularrepresentation
2.5Numberofirreduciblerepresentations
2.6Canonicaldecompositionofarepresentation
2.7Explicitdecompositionofarepresentation

3Subgroups，products，inducedrepresentations
3.1Abeliansubgroups
3.2Productoftwogroups
3.3Inducedrepresentations

4Compactgroups
4.1Compactgroups
4.2lnvariantmeasureonacompactgroup
4.3Linearrepresentationsofcompactgroups

5Examples
5.1ThecyclicGroup
5.2Thegroup
5.3Thedihedralgroup
5.4Thegroup
5.5Thegroup
5.6Thegroup
5.7Thealternatinggroup
5.8Thesymmetricgroup
5.9Thegroupofthecube
Bibliography：PartⅠ

PartⅡ
RepresentationsinCharacteristicZero
6Thegroupalgebra
6.1Representationsandmodules
6.2DecompositionofC[G]
6.3ThecenterofC[G]
6.4Basicpropertiesofintegers
6.5lntegralitypropertiesofcharacters.Applications

7Inducedrepresentations;Mackeyscriterion
7.1Induction
7.2Thecharacterofaninducedrepresentation;
thereciprocityformula
7.3Restrictiontosubgroups
7.4Mackeysirreducibilitycriterion

8Examplesofinducedrepresentations
8.lNormalsubgroups;applicationstothedegreesofthe
ineduciblerepresentations
8.2Semidirectproductsbyanaheliangroup
8.3Areviewofsomeclassesoffinitegroups
8.4Syiowstheorem
8.5Linearrepresentationsofsuperselvablegroups

9Artinstheorem
9.1TheringR(G)
9.2StatementofArtinstheorem
9.3Firstproof
9.4Secondproofof(i)=(ii)

10AtheoremofBrauer
10.1p-regularelements;p-elementarysubgroups
10.2Inducedcharactersarisingfromp-elementary
subgroups
10.3Constructionofcharacters
10.4Proofoftheorems18and18
10.5Brauerstheorem

11ApplicationsofBrauerstheorem
11.1Characterizationofcharacters
11.2AtheoremofFrobenius
11.3AconversetoBrauerstheorem
11.4ThespectrumofAR(G)

12Rationalityquestions
12.1TheringsRK(G)andRK(G)
12.2Schurindices
12.3Realizabilityovercyclotomicfields
12.4TherankofRK(G)
12.5GeneralizationofArtinstheorem
12.6GeneralizationofBrauerstheorem
12.7Proofoftheorem28

13Rationalityquestions：examples
13.IThefieldQ
13.2ThefieldR
Bibliography：PartⅡ

PartⅢ
IntroductiontoBrauerTheory
14ThegroupsRK(G)，R(G)，andPk(G)
14.1TheringsRK(G)andR，(G)
14.2ThegroupsPk(G)andP^(G)
14.3StructureofPk(G)
14.4StructureofPA(G)
14.5Dualities
14.6Scalarextensions

15Thecdetriangle
15.1Definitionofc：Pk(G)——Rk(G)
15.2Definitionofd：Rs(G)——Rk(G)
15.3Definitionofe：Pk(G)——RK(G)
15.4Basicpropertiesofthecdetriangle
15.5Example：p-gmups
15.6Example：p-groups
15.7Example：productsofp-groupsandp-groups

16Theorems
16.1Propertiesofthecdetriangle
16.2Characterizationoftheimageofe
16.3CharacterizationofprojectiveA[G]-modules
bytheircharacters
16.4ExamplesofprojectiveA[G]-modules：irreducible
representationsofdefectzero

17Proofs
17.IChangeofgroups
17.2Brauerstheoreminthemodularcase
17.3Proofoftheorem33
17.4Proofoftheorem35
17.5Proofoftheorem37
17.6Proofoftheorem38

18Modularcharacters
18.1Themodularcharacterofarepresentation
18.2Independenceofmodularcharacters
18.3Reformulations
18.4Asectionford
18.5Example：Modularcharactersofthesymmetricgroup
18.6Example：Modularcharactersofthealternatinggroup

19ApplicationtoArtinrepresentations
19.1ArtinandSwanrepresentations
19.2RationalityoftheArtinandSwanrepresentations
19.3Aninvariant

Appendix
Bibliography：PartⅢ
Indexofnotation
Indexofterminology