李群、李代数和表示论 pdf epub mobi txt 电子书下载 2024

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Brian C. Hall

世界图书出版公司

2007-10

351

43.00元

Graduate Texts in Mathematics

9787506282970

图书标签: 数学李代数李群群论 GTM 代数数学物理表示论

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发表于2024-12-25

李群、李代数和表示论 epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

李群、李代数和表示论 pdf epub mobi txt 电子书下载 2024

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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).

李群、李代数和表示论下载 mobi epub pdf txt 电子书