李群、李代数和表示论txt,chm,pdf,epub,mobi下载 作者:Brian C. Hall 出版社: 世界图书出版公司 原作名: Lie Groups, Lie Algebras, and Representations: An Elementary Introduction 出版年: 2007-10 页数: 351 定价: 43.00元 丛书: Graduate Texts in Mathematics ISBN: 9787506282970
内容简介 · · · · · ·ThisbookprovidesanintroductiontoLiegroups,Liealgebras,andrepresentationtheory,aimedatgraduatestudentsinmathematicsandphysics.Althoughtherearealreadyseveralexcellentbooksthatcovermanyofthesametopics,thisbookhastwodistinctivefeaturesthatIhopewillmakeitausefuladditiontotheliterature.First,ittreatsLiegroups(notjustLiealgebras)inawaythatminimizestheamountofmanifoldtheoryneeded.Thus,...
ThisbookprovidesanintroductiontoLiegroups,Liealgebras,andrepresentationtheory,aimedatgraduatestudentsinmathematicsandphysics.Althoughtherearealreadyseveralexcellentbooksthatcovermanyofthesametopics,thisbookhastwodistinctivefeaturesthatIhopewillmakeitausefuladditiontotheliterature.First,ittreatsLiegroups(notjustLiealgebras)inawaythatminimizestheamountofmanifoldtheoryneeded.Thus,Ineitherassumeapriorcourseondifferentiablemanifoldsnorprovideacon-densedsuchcourseinthebeginningchapters.Second,thisbookprovidesagentleintroductiontothemachineryofsemisimplegroupsandLiealgebrasbytreatingtherepresentationtheoryofSU(2)andSU(3)indetailbeforegoingtothegeneralcase.Thisallowsthereadertoseeroots,weights,andtheWeylgroup"inaction"insimplecasesbeforeconfrontingthegeneraltheory. ThestandardbooksonLietheorybeginimmediatelywiththegeneralcase:asmoothmanifoldthatisalsoagroup.TheLiealgebraisthendefinedasthespaceofleft-invariantvectorfieldsandtheexponentialmappingisdefinedintermsoftheflowalongsuchvectorfields.Thisapproachisundoubtedlytherightoneinthelongrun,butitisratherabstractforareaderencounteringsuchthingsforthefirsttime.Furthermore,withthisapproach,onemusteitherassumethereaderisfamiliarwiththetheoryofdifferentiablemanifolds(whichrulesoutasubstantialpartofone'saudience)oronemustspendconsiderabletimeatthebeginningofthebookexplainingthistheory(inwhichcase,ittakesalongtimetogettoLietheoryproper).
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