李群,李代数及其表示

图书标准信息

• 作者 [美]范阮达若詹 著
• 出版社 世界图书出版公司
• 出版时间 2008-05
• 版次 1
• ISBN 9787506292245
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 430页
• 正文语种 英语
• 原版书名 Lie Groups, Lie Algebras, and Their Representations
• 丛书 Graduate Texts in Mathematics

【内容简介】

《李群，李代数及其表示》是一部学习李群，李代数及其表示论的优秀的研究生教材。与其他一些同类著作相比，《李群，李代数及其表示》有两大特点，第一大特点是：作者以一种尽可能少地运用流形知识的方法来研究李群。这种方法十分清晰易懂，使读者可以快速地掌握知识的核心内容。第二大特点是：《李群，李代数及其表示》在给出半单李群及李代数的理论框架之前，通过详尽地介绍SU(2)和SU(3)的表示理论来引入即将介绍的一般内容，这种方式使得读者能够在了解一般理论之前已经有了对根系、权，及Weyl群的简单认识。同时，书中众多的例子和图示可以很好地协助学习并理解一些内容。《李群，李代数及其表示》分为两部分，第一部分主要介绍了李群与李代数，以及它们之间的相互关系，同时还介绍了基础的表示论。第二部分则阐述了半单李群与李代数理论。
ThisbookisintendedforaoneyeargraduatecourseonLiegroupsandLiealgebras.TheauthorproceedsbeyondtherepresentationtheoryofcompactLiegroups(whichisthebasisofmanytexts)andprovidesacarefullychosenrangeofmaterialtogivethestudentthebiggerpicture.ForcompactLiegroups，thePeter-Weyltheorem，conjugacyofmaximaltori(twoproofs)，Weylcharacterformulaandmorearecovered.Thebookcontinueswiththestudyofcomplexanalyticgroups，thengeneralnoncompactLiegroups，includingtheCoxeterpresentationoftheWeylgroup，theIwasawaandBruhatdecompositions，Cartandecomposition，symmetricspaces，Cayleytransforms，relativerootsystems，Satakediagrams，extendedDynkindiagramsandasurveyofthewaysLiegroupsmaybeembeddedinoneanother.Thebookculminatesina"topics"sectiongivingdepthtothestudentsunderstandingofrepresentationtheory，takingtheFrobenius-Schurdualitybetweentherepresentationtheoryofthesymmetricgroupandtheunitarygroupsasaunifyingtheme，withmanyapplicationsindiverseareassuchasrandommatrixtheory，minorsofToeplitzmatrices，symmetricalgebradecompositions，Gelfandpairs，Heckealgebras，representationsoffinitegenerallineargroupsandthecohomologyofGrassmanniansandflagvarieties.

【目录】

Preface
Chapter1DifferentiableandAnalyticManifolds
1.1DifferentiableManifolds
1.2AnalyticManifolds
1.3TheFrobcniusTheorem
1.4Appendix
Exercises
Chapter2LieGroupsandLieAlgebras
2.1DefinitionandExamplesofLieGroups
2.2LieAlgebras
2.3TheLieAlgebraofaLieGroup
2.4TheEnvelopingAlgebraofaLieGroup
2.5SubgroupsandSubalgebras
2.6LocallyisomorphicGroups
2.7Homomorphisms
2.8TheFundamentalTheoremofLie
2.9ClosedLieSubgroupsandHomogeneousSpaces.OrbitsandSpacesofOrbits
2.10TheExponentialMap
2.11TheUniquenessoftheRealAnalyticStructureofaRealLieGroup
2.12TaylorSeriesExpansionsonaLieGroup
2.13TheAdjointRepresentationsof!~andG
2.14TheDifferentialoftheExponentialMap
2.15TheBaker-CampbelI-HausdorffFormula
2.16LiesTheoryofTransformationGroups
Exercises
Chapter3StructureTheory
3.1ReviewofLinearAlgebra
3.2TheUniversalEnvelopingAlgebraofaLieAlgebra
3.3TheUniversalEnvelopingAlgebraasaFilteredAlgebra
3.4TheEnvelopingAlgebraofaLieGroup
3.5NilpotentLieAlgebras
3.6NilpotentAnalyticGroups
3.7SolvableLieAlgebras
3.8TheRadicalandtheNilRadical
3.9CartansCriteriaforSolvabilityandSemisimplicity
3.10SemisimpleLieAlgebras
3.11TheCasimirElement
3.12SomeCohomology
3.13TheTheoremofWeyl
3.14TheLeviDecomposition
3.15TheAnalyticGroupofaLieAlgebra
3.16ReductiveLieAlgebras
3.17TheTheoremofAdo
3.18SomeGlobalResults
Exercises
Chapter4ComplexSemisimpleLieAlgebrasAndLieGroups:StructureandRepresentation
4.1CartanSubalgebras
4.2TheRepresentationsoft(2,C)
4.3StructureTheory
4.4TheClassicalLieAlgebras
4.5DeterminationoftheSimpleLieAlgebrasoverC
4.6RepresentationswithaHighestWeight
4.7RepresentationsofSemisimpleLieAlgebras
4.8ConstructionofaSemisimpleLieAlgebrafromitsCartanMatrix
……
Bibliogrphy
Index