7_Introduction to Lie Groups and Transformation Groups

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1、LectureNotesinMathematicsAninformalseriesofspeciallectures,seminarsandreportsonmathematicaltopicsEditedbyA.Dold,HeidelbergandB.Eckmann,ZUrich7PhilippeTondeurDepartmentofMathematicsUniversityofZfJrichIntroductiontoLieGroupsandTransformationGroups1965Springer-Verlag.Berli

2、n-Heidelberg.NewYorkAllrights,especiallythatoftranalation/ntoforeignlanguages,reserved.Itisalsoforbiddentoreproducethisbook,eitherwholeorinpart,byphotomechanicalmeans(photostat,microfilmand/ormicrocard)orbyotherprocedurewithoutwrittenpermissionfromSpringerVerlag.@bySprl

3、nger-VerlagBerlin9Heidelberg196~.LibraryofCongressCatalogCardNumber6~--26947.PrintedinGermany.TitleNo.7327PrintedbyBehz,WeinhelmPREFACEThesenoteswerewrittenforintroductorylecturesonLiegroupsandtransformationgroups,heldattheUniversitiesofBuenosAiresandZurich.Thenotionso

4、fadifferentiablemanifold,adifferentiablemapandavectorfieldaresupposedknown.Thereisanappendixoncategoriesandfunctors.ThefirsttwochaptersareinfluencedbyapaperofR.Palais[lg].Insections5.Zand5.3,alotistakenfromS.KobayashiandK.Nomizu[11].Inchapter7,S.Helgason[61wasoftenused.

5、Ofcourse,C.Chevalley[3]wasconstantlyconsulted.Thebibliographyorientsonthevarioussources.Aspecialfeatureofthispresentationisthesystematicavoidanceoftheuseoflocalcoordinatesonamanifold.ThisallowstheuseofthepresentedtheorywithslightmodificationsforLiegroupsoverBanachmanifo

6、lds.Seee.g.B.Maissen[10].June1964PhilippeTondeurCONTENTS.G-Objects.1.1.Definitionandexamples.11.Z.Equivariantmorphisms.71.3.Orbits.13"1.4.ParticularG-sets.23.G-Spaces.Z.1.Definitionandexamples.28Z.Z.Orbitspace.30.G-Manifolds.3.1.DefinitionandexamplesofLiegroups.343.Z.De

7、finitionandexamplesofG-manifolds.37.Vectorfields.4.1.Realfunctions.404.Z.Operatorsandvectorfields.4Z4.3.TheLiealgebraofaLiegroup.464.4.Effectofmapsonoperatorsandvectorfields.504.5.ThefunctorL.5Z4.6.ApplicationsofthefunctoralityofL.594.7.TheadjointrepresentationofaLiegro

8、up.64The*indicatesasection,thelectureofwhichisnotnecessaryfortheunderstandingofthesubsequentdevelopments..Vect