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an elementary introduction to groups and representations

an elementary introduction to groups and representations

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时间：2018-08-01

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

2、eExamplesofGroups33.Subgroups,theCenter,andDirectProducts44.HomomorphismsandIsomorphisms55.Exercises6Chapter2.MatrixLieGroups91.De nitionofaMatrixLieGroup92.ExamplesofMatrixLieGroups103.Compactness154.Connectedness165.Simple-connectedness186.HomomorphismsandIsomorphisms197.L

3、ieGroups208.Exercises22Chapter3.LieAlgebrasandtheExponentialMapping271.TheMatrixExponential272.ComputingtheExponentialofaMatrix293.TheMatrixLogarithm314.FurtherPropertiesoftheMatrixExponential345.TheLieAlgebraofaMatrixLieGroup366.PropertiesoftheLieAlgebra407.TheExponentialMa

4、pping448.LieAlgebras469.TheComplexi cationofaRealLieAlgebra4810.Exercises50Chapter4.TheBaker-Campbell-Hausdor Formula531.TheBaker-Campbell-Hausdor FormulafortheHeisenbergGroup532.TheGeneralBaker-Campbell-Hausdor Formula563.TheSeriesFormoftheBaker-Campbell-Hausdor Formula634.

5、SubgroupsandSubalgebras645.Exercises65Chapter5.BasicRepresentationTheory671.Representations672.WhyStudyRepresentations?69iiiivCONTENTS3.ExamplesofRepresentations704.TheIrreducibleRepresentationsofsu(2)755.DirectSumsofRepresentationsandCompleteReducibility796.TensorProductsof

6、Representations827.Schur'sLemma868.GroupVersusLieAlgebraRepresentations889.CoveringGroups9410.Exercises96Chapter6.TheRepresentationsofSU(3),andBeyond1011.Preliminaries1012.WeightsandRoots1033.HighestWeightsandtheClassi cationTheorem1054.ProofoftheClassi cationTheorem1075.AnE

7、xample:HighestWeight(1;1)1116.TheWeylGroup1127.ComplexSemisimpleLieAlgebras1158.Exercises117Chapter7.Cumulativeexercises119Chapter8.Bibliography1211.PREFACEv1.PrefaceThesenotesaretheoutgrowthofagraduatecourseonLiegroupsItaughtattheUniversityofVirginiain1994.Intryingto ndatex

8、tforthecourseIdiscoveredthatbooksonLiegroupseitherpresupposeaknowledgeofdi

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