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an elementary introduction to groups and representations

an elementary introduction to groups and representations

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页数：128页

时间：2018-07-29

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1、AnElementaryIntroductiontoGroupsandRepresentationsBrianC.HallAuthoraddress:UniversityofNotreDame,DepartmentofMathematics,NotreDameIN46556USAE-mailaddress:bhall@nd.eduarXiv:math-ph/000503231May2000Contents1.PrefaceiiChapter1.Groups11.De nitionofaGroup,andBasicProperties12.SomeExamplesofG

2、roups33.Subgroups,theCenter,andDirectProducts44.HomomorphismsandIsomorphisms55.Exercises6Chapter2.MatrixLieGroups91.De nitionofaMatrixLieGroup92.ExamplesofMatrixLieGroups103.Compactness154.Connectedness165.Simple-connectedness186.HomomorphismsandIsomorphisms197.LieGroups208.Exercises22C

3、hapter3.LieAlgebrasandtheExponentialMapping271.TheMatrixExponential272.ComputingtheExponentialofaMatrix293.TheMatrixLogarithm314.FurtherPropertiesoftheMatrixExponential345.TheLieAlgebraofaMatrixLieGroup366.PropertiesoftheLieAlgebra407.TheExponentialMapping448.LieAlgebras469.TheComplexi

4、cationofaRealLieAlgebra4810.Exercises50Chapter4.TheBaker-Campbell-Hausdor Formula531.TheBaker-Campbell-Hausdor FormulafortheHeisenbergGroup532.TheGeneralBaker-Campbell-Hausdor Formula563.TheSeriesFormoftheBaker-Campbell-Hausdor Formula634.SubgroupsandSubalgebras645.Exercises65Chapter5.B

5、asicRepresentationTheory671.Representations672.WhyStudyRepresentations?69iiiivCONTENTS3.ExamplesofRepresentations704.TheIrreducibleRepresentationsofsu(2)755.DirectSumsofRepresentationsandCompleteReducibility796.TensorProductsofRepresentations827.Schur'sLemma868.GroupVersusLieAlgebraRepr

6、esentations889.CoveringGroups9410.Exercises96Chapter6.TheRepresentationsofSU(3),andBeyond1011.Preliminaries1012.WeightsandRoots1033.HighestWeightsandtheClassi cationTheorem1054.ProofoftheClassi cationTheorem1075.AnExample:HighestWeight(1;1)1116.TheWeylGroup1127.ComplexSemisimpleLieAlgeb

7、ras1158.Exercises117Chapter7.Cumulativeexercises119Chapter8.Bibliography1211.PREFACEv1.PrefaceThesenotesaretheoutgrowthofagraduatecourseonLiegroupsItaughtattheUniversityofVirginiain1994.Intryingto ndatextforthecourseIdiscoveredthatbooksonLiegroupseitherpresupposeaknowledgeofdi

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