5.lie.groups.and.algebraic.groups.iii.-.a..l..onishchik,.e..b..vinberg

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1、A.L.OnishchikE.B.Vinberg(Eds.)’I7i?‘;LieGroupsandLieAlgebrasIIIStructureofLieGroupsandLieAlgebrasSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestEncyclopaediaofMathematicalSciencesVolume41Editor-in-Chief:RXGamkrelidzeStructureofLieGroupsandLieAlgebrasV.V.Gorbatsev

2、ich,A.L.Onishchik,E.B.VinbergTranslatedfromtheRussianbyV.MinachinContentsIntroduction........................7Chapter1.GeneralTheorems....................851.Lie’sandEngel’sTheorems...................81.1.Lie’sTheorem......................81.2.GeneralizationsofLie’sTheorem.............101.3.Eng

3、el’sTheoremandCorollariestoIt...........111.4.AnAnalogueofEngel’sTheoreminGroupTheory....1252.TheCartanCriterion......................132.1.InvariantBilinearForms.................132.2.CriteriaofSolvabilityandSemisimplicity.........132.3.FactorizationintoSimpleFactors.............14$3.CompleteR

4、educibilityofRepresentationsandTrivialityoftheCohomologyofSemisimpleLieAlgebras.........153.1.CohomologicalCriterionofCompleteReducibility.....153.2.TheCasimirOperator..................153.3.TheoremsontheTrivialityofCohomology........163.4.CompleteReducibilityofRepresentations.........163.5.Red

5、uctiveLieAlgebras..................1734.LeviDecomposition......................184.1.Levi’sTheorem......................184.2.ExistenceofaLieGroupwithaGivenTangentAlgebra..194.3.Malcev’sTheorem....................204.4.ClassificationofLieAlgebraswithaGivenRadical....2055.LinearLieGroups........

6、...............212Contents5.1.BasicNotions.......................215.2.SomeExamples......................225.3.Ado’sTheorem......................245.4.CriteriaofLinearizabilityforLieGroups.Linearizer....245.5.SufficientLinearizabilityConditions............255.6.StructureofLinearLieGroups.......

7、.......27§6.LieGroupsandAlgebraicGroups................276.1.ComplexandRealAlgebraicGroups...........276.2.AlgebraicSubgroupsandSubalgebras...........286.3.SemisimpleandReductiveAlgebraicGroups........296.4.PolarDecomposition.....