有限群的线性表示
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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
装帧平装
货号131
上书时间2024-08-15
商品详情
- 品相描述:八五品
图书标准信息
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作者
[法]赛尔 著
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出版社
世界图书出版公司
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出版时间
2008-10
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版次
1
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ISBN
9787506292597
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定价
35.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
170页
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正文语种
英语
- 【内容简介】
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《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】
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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
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