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1、AlgebraicGroups,LieGroups,andtheirArithmeticSubgroupsJ.S.MilneVersion3.00April1,2011Thisworkisamodernexpositionofthetheoryofalgebraicgroups(affinegroupschemes),Liegroups,andtheirarithmeticsubgroups.BibTeXinformation:@misc{milneALA,author={Milne,JamesS.},title={AlgebraicGroups,LieGroups,andth
2、eirArithmeticSubgroups},year={2011},note={Availableatwww.jmilne.org/math/}}v1.00April29,2009.Firstversionontheweb(firsttwochaptersonly).v1.01May10,2009.Minorfixes.v1.02June1,2009.Moreminorfixes.v2.00April27,2010.Postedall6chapters(378pages).v3.00April1,2011.Revisedandexpanded(422pages).Pleases
3、endcommentsandcorrectionstomeattheaddressonmywebsitehttp://www.jmilne.org/math/.ThephotoisofthefamouslaughingBuddhaonThePeakThatFlewHere,Hangzhou,Zhejiang,China.Copyrightc2005,2006,2009,2010,2011J.S.Milne.Singlepapercopiesfornoncommercialpersonalusemaybemadewithoutexplicitpermis-sionfromthe
4、copyrightholder.TableofContentsTableofContents3Preface........................................5IBasicTheoryofAffineGroups131Introductoryoverview.............................142Definitions...................................183Examples...................................294Somebasicconstructions
5、...........................345AffinegroupsandHopfalgebras.......................416Affinegroupsandaffinegroupschemes...................537Grouptheory:subgroupsandquotientgroups.................738Representationsofaffinegroups.......................949Grouptheory:theisomorphismtheorems..........
6、........12110Recoveringagroupfromitsrepresentations;Jordandecompositions....12811Characterizationsofcategoriesofrepresentations..............13712Finiteflataffinegroups............................14413Theconnectedcomponentsofanalgebraicgroup..............15214Groupsofmultiplicativetype;tori..
7、....................16315Unipotentaffinegroups............................17616Solvableaffinegroups.............................18317Thestructureofalgebraicgroups.......................19418Example:thespingroups...........................20319Theclassicals
