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[法] 赛尔 著 / 世界图书出版公司 / 2008-10 / 平装
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有限群的线性表示
《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。
PartⅠRepresentationsandCharacters1Generalitiesonlinearrepresentations1.1Definitions1.2Basicexamples1.3Submpmsentations1.4Irreduciblerepresentations1.5Tensorproductoftworepresentations1.6Symmetricsquareandalternatingsquare2Charactertheory2.1Thecharacterofarepresentation2.2Schurslemma;basicapplications2.30rthogonalityrelationsforcharacters2.4Decompositionoftheregularrepresentation2.5Numberofirreduciblerepresentations2.6Canonicaldecompositionofarepresentation2.7Explicitdecompositionofarepresentation3Subgroups,products,inducedrepresentations3.1Abeliansubgroups3.2Productoftwogroups3.3Inducedrepresentations4Compactgroups4.1Compactgroups4.2lnvariantmeasureonacompactgroup4.3Linearrepresentationsofcompactgroups5Examples5.1ThecyclicGroup5.2Thegroup5.3Thedihedralgroup5.4Thegroup5.5Thegroup5.6Thegroup5.7Thealternatinggroup5.8Thesymmetricgroup5.9ThegroupofthecubeBibliography:PartⅠPartⅡRepresentationsinCharacteristicZero6Thegroupalgebra6.1Representationsandmodules6.2DecompositionofC[G]6.3ThecenterofC[G]6.4Basicpropertiesofintegers6.5lntegralitypropertiesofcharacters.Applications7Inducedrepresentations;Mackeyscriterion7.1Induction7.2Thecharacterofaninducedrepresentation;thereciprocityformula7.3Restrictiontosubgroups7.4Mackeysirreducibilitycriterion8Examplesofinducedrepresentations8.lNormalsubgroups;applicationstothedegreesoftheineduciblerepresentations8.2Semidirectproductsbyanaheliangroup8.3Areviewofsomeclassesoffinitegroups8.4Syiowstheorem8.5Linearrepresentationsofsuperselvablegroups9Artinstheorem9.1TheringR(G)9.2StatementofArtinstheorem9.3Firstproof9.4Secondproofof(i)=(ii)10AtheoremofBrauer10.1p-regularelements;p-elementarysubgroups10.2Inducedcharactersarisingfromp-elementarysubgroups10.3Constructionofcharacters10.4Proofoftheorems18and1810.5Brauerstheorem11ApplicationsofBrauerstheorem11.1Characterizationofcharacters11.2AtheoremofFrobenius11.3AconversetoBrauerstheorem11.4ThespectrumofAR(G)12Rationalityquestions12.1TheringsRK(G)andRK(G)12.2Schurindices12.3Realizabilityovercyclotomicfields12.4TherankofRK(G)12.5GeneralizationofArtinstheorem12.6GeneralizationofBrauerstheorem12.7Proofoftheorem2813Rationalityquestions:examples13.IThefieldQ13.2ThefieldRBibliography:PartⅡPartⅢIntroductiontoBrauerTheory14ThegroupsRK(G),R(G),andPk(G)14.1TheringsRK(G)andR,(G)14.2ThegroupsPk(G)andP^(G)14.3StructureofPk(G)14.4StructureofPA(G)14.5Dualities14.6Scalarextensions15Thecdetriangle15.1Definitionofc:Pk(G)——Rk(G)15.2Definitionofd:Rs(G)——Rk(G)15.3Definitionofe:Pk(G)——RK(G)15.4Basicpropertiesofthecdetriangle15.5Example:p-gmups15.6Example:p-groups15.7Example:productsofp-groupsandp-groups16Theorems16.1Propertiesofthecdetriangle16.2Characterizationoftheimageofe16.3CharacterizationofprojectiveA[G]-modulesbytheircharacters16.4ExamplesofprojectiveA[G]-modules:irreduciblerepresentationsofdefectzero17Proofs17.IChangeofgroups17.2Brauerstheoreminthemodularcase17.3Proofoftheorem3317.4Proofoftheorem3517.5Proofoftheorem3717.6Proofoftheorem3818Modularcharacters18.1Themodularcharacterofarepresentation18.2Independenceofmodularcharacters18.3Reformulations18.4Asectionford18.5Example:Modularcharactersofthesymmetricgroup18.6Example:Modularcharactersofthealternatinggroup19ApplicationtoArtinrepresentations19.1ArtinandSwanrepresentations19.2RationalityoftheArtinandSwanrepresentations19.3AninvariantAppendixBibliography:PartⅢIndexofnotationIndexofterminology
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