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1、August,1999MonstrousMoonshineandtheClassi cationofCFT(16lecturesgiveninIstanbul,August1998)TerryGannonDepartmentofMathematicalSciences,UniversityofAlberta,Edmonton,Alberta,Canada,T6G2G1e-mail:tgannon@math.ualberta.caAbstractInthesenoteswegiveanintroductionbothtoMonstrousMoo
2、nshineandtotheclassi ca-tionofrationalconformal eldtheories,usingthisasanexcusetoexploreseveralrelatedstructuresandgoonalittletourofmodernmath.WewilldiscussLiealgebras,modularfunctions,the nitesimplegroupclassi cation,vertexoperatoralgebras,Fermat'sLastTheorem,categorytheor
3、y,(generalised)Kac-Moodyalgebras,denominatoridentities,theA-D-Emeta-pattern,representationsofanealgebras,Galoistheory,etc.Thisworkisinformalandpedagogical,andaimedmostlyatgradstudentsinmathormathphys,butIhopethatmanyinterestednonexpertswill ndsomethingofvaluehere
4、likeanygo
5、odWaltDisneymovieItrynottocompletelyignorethe`grown-ups'.Myemphasisisonideasandmotivations,sothesenotesareintendedtocomplementotherpapersandbookswherethismaterialispresentedwithmoretechnicaldetail.Thelevelofdicultyvariessigni cantlyfromtopictotopic.Thetwoparts
6、infactanyoft
7、hesections
8、canbereadindependently.arXiv:math.QA/9906167v210Aug1999TableofContentsPart1.Theclassi cationofconformal eldtheories1.1.Informalmotivation...........................11.2.Liealgebras..............................41.3.Representationsof nite-dimensionalsimpleLiealgeb
9、ras...........101.4.AnealgebrasandtheKac-Petersonmatrices...............131.5.Theclassi cationofphysicalinvariants..................171.6.TheA-D-Emeta-pattern.........................191.7.Simple-currentsandcharge-conjugation..................241.8.Galoistheory............
10、..................281.9.Themodernapproachtoclassifyingphysicalinvariants...........31Part2.MonstrousMoonshine2.1.Introduction..............................352.2.Ingredient#1:FinitesimplegroupsandtheMonster............382.3.Ingredient#2:ModularfunctionsandHauptmoduls........
11、....402.4.TheMonstrousMoonshineconjectures...................462.5.Formalpowerseri
