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[美] 贝克 著 / 清华大学出版社 / 2009-11 / 平装
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Springer大学数学图书·矩阵群:李群理论基础(影印版)
本书讲述李群和李代数基础理论,内容先进,讲述方法科学,易于掌握和使用。书中有大量例题和习题(附答案或提示),便于阅读。适合用作大学数学系和物理系高年级本科生选修课教材、研究生课程教材或参考书。
PartⅠ.BasicIdeasandExamples1.RealandComplexMatrixGroups1.1GroupsofMatrices1.2GroupsofMatricesasMetricSpaces1.3Compactness1.4MatrixGroups1.5SomeImportantExamples1.6ComplexMatricesasRealMatrices1.7ContinuousHomomorphismsofMatrixGroups1.8MatrixGroupsforNormedVectorSpaces1.0ContinuousGroupActions2.Exponentials,DifferentialEquationsandOne-parameterSubgroups2.1TheMatrixExponentialandLogarithm2.2CalculatingExponentialsandJordanForm2.3DifferentialEquationsinMatrices2.4One-parameterSubgroupsinMatrixGroups2.5One-parameterSubgroupsandDifferentialEquations3.TangentSpacesandLieAlgebras3.1LieAlgebras.3.2Curves,TangentSpacesandLieAlgebras3.4SomeObservationsontheExponentialFunctionofaMatrixGroup3.5SO(3)andSU(2)3.6TheComplexificationofaRealLieAlgebra4.Algebras,QuaternionsandQuaternionicSymplecticGroups4.1Algebras4.2RealandComplexNormedAlgebras4.3LinearAlgebraoveraDivisionAlgebra4.4TheQuaternions4.5QuaternionicMatrixGroups4.6AutomorphismGroupsofAlgebras5.CliffordAlgebrasandSpinorGroups5.1RealCliffordAlgebras5.2CliffordGroups5.3PinorandSpinorGroups5.4TheCentresofSpinorGroups5.5FiniteSubgroupsofSpinorGroups6.LorentzGroups6.1LorentzGroups6.2APrincipalAxisTheoremforLorentzGroups6.3SL2(C)andtheLorentzGroupLor(3,1)PartⅡ.MatrixGroupsasLieGroups7.LieGroups7.1SmoothManifolds7.2TangentSpacesandDerivatives7.3LieGroups7.4SomeExamplesofLieGroups7.5SomeUsefulFormulaeinMatrixGroups7.6MatrixGroupsareLieGroups7.7NotAllLieGroupsareMatrixGroups8.HomogeneousSpaces8.1HomogeneousSpacesasManifolds8.2HomogeneousSpacesasOrbits8.3ProjectiveSpaces8.4Grassmannians8.5TheGram-SchmidtProcess8.6ReducedEchelonForm8.7RealInnerProducts8.8SymplecticForms9.ConnectivityofMatrixGroups9.1ConnectivityofManifolds9.2ExamplesofPathConnectedMatrixGroups9.3ThePathComponentsofaLieGroup9.4AnotherConnectivityResultPartⅢ.CompactConnectedLieGroupsandtheirClassification10.MaximalToriinCompactConnectedLieGroups10.1Tori10.2MaximalToriinCompactLieGroups10.3TheNormaliserandWeylGroupofaMaximalTorus10.4TheCentreofaCompactConnectedLieGroup11.Semi-simpleFactorisation11.1AnInvariantInnerProduct11.2TheCentreanditsLieAlgebra11.3LieIdealsandtheAdjointAction11.4Semi-simpleDecompositions11.5StructureoftheAdjointRepresentation12.RootsSystems,WeylGroupsandDynkinDiagrams12.1InnerProductsandDuality12.2RootssystemsandtheirWeylgroups12.3SomeExamplesofRootSystems12.4TheDynkinDiagramofaRootSystem12.5IrreducibleDynkinDiagrams12.6FromRootSystemstoLieAlgebrasHintsandSolutionstoSelectedExercisesBibliographyIndex
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