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作者: [德] 著
出版社: 世界图书出版公司
2011-01
版次: 1
ISBN: 9787510029592
定价: 39.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 320页
正文语种: 英语
原版书名: The Classical Groups: Their Invariants and Representations
分类: 自然科学
36人买过
  • Eversincetheyear1925，whenIsucceededindeterminingthecharactersofthesemi-simplecontinuousgroupsbyacombinationofE.Cartansinfini-tesimalmethodsandI.Schursintegralprocedure，Ihavelookedtowardthegoalofderivingthedecisiveresultsforthemostimportantofthesegroupsbydirectalgebraicconstruction，inparticularforthefullgroupofallnon-singu-larlineartransformationsandfortheorthogonalgroup.OwingmainlytoR.Brauersinterventionandcollaborationduringthelastfewyears，itnowappearsthatIhaveinmyhandsallthetoolsnecessaryforthispurpose.Thetaskmaybecharacterizedpreciselyasfollows：withrespecttotheassignedgroupoflineartransformationsintheunderlyingvectorspace，todecomposethespaceoftensorsofgivenrankintoitsirreducibleinvariantsubspaces. TABLEOFCONTENTS
    PREFACETOTHEFIRSTEDITION
    PREFACETOTHESECONDEDITION
    CHAPTERI
    INTRODUCTION
    1.Fields，rings，ideals，polynomials
    2.Vectorspace
    3.Orthogonaltransformations，Euclideanvectorgeometry
    4.Groups，KleinsErlangerprogram..Quantities
    5.Invariantsandcovariants
    CHAPTERII
    VECTORINVARIANTS
    1.Remembranceofthingspast
    2.Themainpropositionsofthetheoryofinvariants
    A.FrostMAINTHEOREM
    3.Firstexample：thesymmetricgroup
    4.Capellisidentity
    5.ReductionofthefirstmainproblembymeansofCapellisidentities
    6.Secondexample：theunimodulargroup，.qL（n）
    7.Extensiontheorem.Thirdexample：thegroupofsteptransformations
    8.Ageneralmethodforincludingeontravariantarguments
    9.Fourthexample：theorthogonalgroup
    B.ACLOSE-UPOFTHEORTHOGONALGROUP
    10.Cayleysrationalparametrizationoftheorthogonalgroup
    11，Formalorthogonalinvariants
    12.Arbitrarymetricgroundform
    13.Theinfinitesimalstandpoint
    C.THESECONDMAINTHEOREM
    14.Statementofthepropositionfortheunimodulargroup
    15.Capellisformalcongruence
    16.Proofofthesecondmaintheoremfortheunimodulargroup
    17.Thesecondmaintheoremfortheunimodulargroup
    CHAPTERIII
    MATRICALGEBRASANDGROUPRINGS
    A.THEORYOFFULLYREDUCIBLEMATRICALGEBRAS
    1.Fundamentalnotionsconcerningmatricalgebras.TheSchurlemma
    2.Preliminaries
    3.Representationsofasimplealgebra
    4.Wedderburnstheorem
    5.Thefullyreduciblematricalgebraanditscommutatoralgebra
    B.THERINGOFAFINITEGROUPANDITSCOMMUTATORALGEBRA
    6.Statingtheproblem
    7.Fullreducibilityofthegroupring
    TABLEOFCONTENTS
    8.Formallemmas.
    9.Reciprocitybetweengroupringandcommutatoralgebra
    10.Ageneralization
    CHAPTERIV
    THESYMMETRICGROUPANDTHEFULLLINEARGROUP
    1.Representationofafinitegroupinanalgebraicallyclosedfield
    2.TheYoungsymmetrizers.Acombinatoriallsmma
    3.Theirreduciblerepresentationsofthesymmetricgroup
    4.Decompositionoftensorspace
    5.Quantities.Expansion
    CHAPTERV
    THEORTHOGONALGROUP
    A.THEENVELOPINGALGEBRAANDTHEORTHOGONALIDEAL
    1.Vectorinvariantsoftheunimodulargroupagain
    2.Theenvelopingalgebraoftheorthogonalgroup
    3.Givingtheresultitsformalsetting
    4.Theorthogonalprimeideal
    5.Anabstractalgebrarelatedtotheorthogonalgroup
    B.THEIRREDUCIBLEREPRESENTATIONS
    6.Decompositionbythetraceoperation
    7.Theirreduciblerepresentationsofthefullorthogonalgroup
    C.THEPROPERORTHOGONALGROUP
    8.Cliffordstheorem
    9.Representationsoftheproperorthogonalgroup
    CHAPTERVI
    THESYMPLECTICGROUP
    1.Vectorinvariantsofthesymplecticgroup
    2.Parametrizationandunitaryrestriction
    3.Embeddingalgebraandrepresentationsofthesymplecticgroup
    CHAPTERVII
    CHARACTERS
    1.Preliminariesaboutunitarytransformations
    2.Characterforsymmetrizationoralternationalone
    3.Averagingoveragroup
    4.Thevolumeelementoftheunitarygroup
    5.Computationofthecharacters
    6.ThecharactersofGL（n）.Enumerationofcovariants
    7.Apurelyalgebraicapproach
    8.Charactersofthesymplecticgroup
    9.Charactersoftheorthogonalgroup
    10.DecompositionandX-multiplication
    11.ThePoinear~polynomial
    ……
  • 内容简介:
    Eversincetheyear1925，whenIsucceededindeterminingthecharactersofthesemi-simplecontinuousgroupsbyacombinationofE.Cartansinfini-tesimalmethodsandI.Schursintegralprocedure，Ihavelookedtowardthegoalofderivingthedecisiveresultsforthemostimportantofthesegroupsbydirectalgebraicconstruction，inparticularforthefullgroupofallnon-singu-larlineartransformationsandfortheorthogonalgroup.OwingmainlytoR.Brauersinterventionandcollaborationduringthelastfewyears，itnowappearsthatIhaveinmyhandsallthetoolsnecessaryforthispurpose.Thetaskmaybecharacterizedpreciselyasfollows：withrespecttotheassignedgroupoflineartransformationsintheunderlyingvectorspace，todecomposethespaceoftensorsofgivenrankintoitsirreducibleinvariantsubspaces.
  • 目录:
    TABLEOFCONTENTS
    PREFACETOTHEFIRSTEDITION
    PREFACETOTHESECONDEDITION
    CHAPTERI
    INTRODUCTION
    1.Fields，rings，ideals，polynomials
    2.Vectorspace
    3.Orthogonaltransformations，Euclideanvectorgeometry
    4.Groups，KleinsErlangerprogram..Quantities
    5.Invariantsandcovariants
    CHAPTERII
    VECTORINVARIANTS
    1.Remembranceofthingspast
    2.Themainpropositionsofthetheoryofinvariants
    A.FrostMAINTHEOREM
    3.Firstexample：thesymmetricgroup
    4.Capellisidentity
    5.ReductionofthefirstmainproblembymeansofCapellisidentities
    6.Secondexample：theunimodulargroup，.qL（n）
    7.Extensiontheorem.Thirdexample：thegroupofsteptransformations
    8.Ageneralmethodforincludingeontravariantarguments
    9.Fourthexample：theorthogonalgroup
    B.ACLOSE-UPOFTHEORTHOGONALGROUP
    10.Cayleysrationalparametrizationoftheorthogonalgroup
    11，Formalorthogonalinvariants
    12.Arbitrarymetricgroundform
    13.Theinfinitesimalstandpoint
    C.THESECONDMAINTHEOREM
    14.Statementofthepropositionfortheunimodulargroup
    15.Capellisformalcongruence
    16.Proofofthesecondmaintheoremfortheunimodulargroup
    17.Thesecondmaintheoremfortheunimodulargroup
    CHAPTERIII
    MATRICALGEBRASANDGROUPRINGS
    A.THEORYOFFULLYREDUCIBLEMATRICALGEBRAS
    1.Fundamentalnotionsconcerningmatricalgebras.TheSchurlemma
    2.Preliminaries
    3.Representationsofasimplealgebra
    4.Wedderburnstheorem
    5.Thefullyreduciblematricalgebraanditscommutatoralgebra
    B.THERINGOFAFINITEGROUPANDITSCOMMUTATORALGEBRA
    6.Statingtheproblem
    7.Fullreducibilityofthegroupring
    TABLEOFCONTENTS
    8.Formallemmas.
    9.Reciprocitybetweengroupringandcommutatoralgebra
    10.Ageneralization
    CHAPTERIV
    THESYMMETRICGROUPANDTHEFULLLINEARGROUP
    1.Representationofafinitegroupinanalgebraicallyclosedfield
    2.TheYoungsymmetrizers.Acombinatoriallsmma
    3.Theirreduciblerepresentationsofthesymmetricgroup
    4.Decompositionoftensorspace
    5.Quantities.Expansion
    CHAPTERV
    THEORTHOGONALGROUP
    A.THEENVELOPINGALGEBRAANDTHEORTHOGONALIDEAL
    1.Vectorinvariantsoftheunimodulargroupagain
    2.Theenvelopingalgebraoftheorthogonalgroup
    3.Givingtheresultitsformalsetting
    4.Theorthogonalprimeideal
    5.Anabstractalgebrarelatedtotheorthogonalgroup
    B.THEIRREDUCIBLEREPRESENTATIONS
    6.Decompositionbythetraceoperation
    7.Theirreduciblerepresentationsofthefullorthogonalgroup
    C.THEPROPERORTHOGONALGROUP
    8.Cliffordstheorem
    9.Representationsoftheproperorthogonalgroup
    CHAPTERVI
    THESYMPLECTICGROUP
    1.Vectorinvariantsofthesymplecticgroup
    2.Parametrizationandunitaryrestriction
    3.Embeddingalgebraandrepresentationsofthesymplecticgroup
    CHAPTERVII
    CHARACTERS
    1.Preliminariesaboutunitarytransformations
    2.Characterforsymmetrizationoralternationalone
    3.Averagingoveragroup
    4.Thevolumeelementoftheunitarygroup
    5.Computationofthecharacters
    6.ThecharactersofGL（n）.Enumerationofcovariants
    7.Apurelyalgebraicapproach
    8.Charactersofthesymplecticgroup
    9.Charactersoftheorthogonalgroup
    10.DecompositionandX-multiplication
    11.ThePoinear~polynomial
    ……
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