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2024-06-15

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

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李群、李代数和表示论 pdf epub mobi txt 电子书下载

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用户评价

评分☆☆☆☆☆

这才是李理论的入门读物

评分☆☆☆☆☆

The Baker-Campbell-Hausdorff Formula（shows that all the information about the group product, at least near the identity, is "encoded" in the Lie ）替代了the Frobenius theorem证明, 证明李代数同构那么李群局部同构

评分☆☆☆☆☆

非常易懂，命题证明命题证明一条一条地来，适合咱学物理的