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1、SpringerMonographsinMathematicsForfurthervolumes:www.springer.com/series/3733JoachimHilgertKarl-HermannNeebStructureandGeometryofLieGroupsJoachimHilgertKarl-HermannNeebMathematicsInstituteDepartmentofMathematicsUniversityofPaderbornFriedrich-AlexanderUniversit?tWarburgerstr.100Erlangen-Nürn
2、berg33095PaderbornCauerstrasse11Germany91054Erlangenhilgert@math.uni-paderborn.deGermanyneeb@mi.uni-erlangen.deISSN1439-7382SpringerMonographsinMathematicsISBN978-0-387-84793-1e-ISBN978-0-387-84794-8DOI10.1007/978-0-387-84794-8SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlN
3、umber:2011942060MathematicsSubjectClassi?cation(2010):7Bxx,22Exx,22Fxx?SpringerScience+BusinessMedia,LLC2012Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exce
4、ptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,
5、andsimilarterms,eveniftheyarenotidenti?edassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)PrefaceNowadaysthereareplentyoftextbooksonLiegroupstochoosefrom,sowefee
6、lweshouldexplainwhywedecidedtoaddanotheronetotherow.MostofthereadilyavailablebooksonLiegroupseitheraimatanelementaryin-troductionmostlyrestrictedtomatrixgroups,orelsetheytrytoprovidethebackgroundonsemisimpleLiegroupsneededinharmonicanalysisandunitaryrepresentationtheorywithaslittlegeneralthe
7、oryaspossible.In[HN91],wetriedtoexhibitthebasicprinciplesofLietheoryratherthanspeci?cmaterial,stressingtheexponentialfunctionasthemeansoftrans-latingproblemsandsolutionsbetweentheglobalandthein?nitesimallevel.Inthatbook,writteninGermanforGermanstud
