李群、李代数和表示论

图书标准信息

• 作者 Brian 著
• 出版社 世界图书出版公司
• 出版时间 2007-10
• 版次 1
• ISBN 9787506282970
• 定价 43.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 351页
• 原版书名 Lie Groups, Lie Algebras, and Representations: An Elementary Introduction

【内容简介】

　　ThisbookprovidesanintroductiontoLiegroups，Liealgebras，andrepresentationtheory，aimedatgraduatestudentsinmathematicsandphysics.Althoughtherearealreadyseveralexcellentbooksthatcovermanyofthesametopics，thisbookhastwodistinctivefeaturesthatIhopewillmakeita　usefuladditiontotheliterature.First，ittreatsLiegroups(notjustLiealgebras)inawaythatminimizestheamountofmanifoldtheoryneeded.Thus，Ineitherassumeapriorcourseondifferentiablemanifoldsnorprovideacon-densedsuchcourseinthebeginningchapters.Second，thisbookprovidesagentleintroductiontothemachineryofsemisimplegroupsandLiealgebrasby　treatingtherepresentationtheoryofSU(2)andSU(3)indetailbeforegoingtothegeneralcase.Thisallowsthereadertoseeroots，weights，andtheWeylgroup"inaction"insimplecasesbeforeconfrontingthegeneraltheory.
　　ThestandardbooksonLietheorybeginimmediatelywiththegeneralcase：asmoothmanifoldthatisalsoagroup.TheLiealgebraisthendefinedasthespaceofleft-invariantvectorfieldsandtheexponentialmappingisdefinedintermsoftheflowalongsuchvectorfields.Thisapproachisundoubtedlytherightoneinthelongrun，butitisratherabstractforareaderencounteringsuchthingsforthefirsttime.Furthermore，withthisapproach，onemusteitherassumethereaderisfamiliarwiththetheoryofdifferentiablemanifolds(whichrulesoutasubstantialpartofonesaudience)oronemustspendconsiderabletimeatthebeginningofthebookexplainingthistheory(inwhichcase，ittakesalongtimetogettoLietheoryproper).

【目录】

PartIGeneralTheory
MatrixLieGroups
1.1DefinitionofaMatrixLieGroup
1.2ExamplesofMatrixLieGroups
1.3Compactness
1.4Connectedness
1.5SimpleConnectedness
1.6HomomorpliismsandIsomorphisms
1.7ThePolarDecompositionforS[(n;R)andSL(n;C)
1.8LieGroups
1.9Exercises
2LieAlgebrasandtheExponentialMapping
2.1TheMatrixExponential
2.2ComputingtheExponentialofaMatrix
2.3TheMatrixLogarithm
2.4FurtherPropertiesoftheMatrixExponential
2.5TheLieAlgebraofaMatrixLieGroup
2.6PropertiesoftheLieAlgebra
2.7TheExponentialMapping
2.8LieAlgebras
2.8.1Structureconstants
2.8.2Directsums
2.9TheComplexificationofaRealLieAlgebra
2.10Exercises
3TheBaker-Campbell-HausdorffFormula
4BasicRepresentationTheory
PartIISemistmpleTheory
References
Index