量子群入门

图书标准信息

• 作者 [美]沙里 著
• 出版社 世界图书出版公司
• 出版时间 2010-04
• 版次 1
• ISBN 9787510005770
• 定价 75.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 654页
• 正文语种 英语

【内容简介】

　　quantumgroupsfirstaroseinthephysicsliterature,particularlyintheworkofL.D.FaddeevandtheLeningradschool,fromtheinversescatteringmethod,whichhadbeendevelopedtoconstructandsolveintegrablequantumsystems.Theyhaveexcitedgreatinterestinthepastfewyearsbecauseoftheirunexpectedconnectionswithsuch,atfirstsight,unrelatedpartsofmathematicsastheconstructionofknotinvariantsandtherepresentationtheoryofalgebraicgroupsincharacteristicp.
　　Intheiroriginalform,quantumgroupsareassociativealgebraswhosedefin-ingrelationsareexpressedintermsofamatrixofconstants(dependingontheintegrablesystemunderconsideration)calledaquantumR-matrix.ItwasrealizedindependentlybyV.G.DrinfeldandM.Jimboaround1985thatthesealgebrasareHopfalgebras,which,inmanycases,aredeformationsofuniversalenvelopingalgebrasofLiealgebras.Alittlelater,Yu.I.ManinandS.L.Woronowiczindependentlyconstructednon-commutativedeforma-tionsofthealgebraoffunctionsonthegroupsSL2(C)andSU2,respectively,andshowedthatmanyoftheclassicalresultsaboutalgebraicandtopologicalgroupsadmitanaloguesinthenon-commutativecase.

【作者简介】

作者：（美国）沙里（Chari.V.）

【目录】

Introduction
1Poisson-LiegroupsandLiebialgebras
1.1Poissonmanifolds
ADefinitions
BFunctorialproperties
CSymplecticleaves
1.2Poisson-Liegroups
ADefinitions
BPoissonhomogeneousspaces
1.3Liebialgebras
ATheLiebialgebraofaPoisson-Liegroup
BMartintriples
CExamples
DDerivations
1.4Dualsanddoubles
ADualsofLiebialgebrasandPoisson-Liegroups
BTheclassicaldouble
CCompactPoisson-Liegroups
1.5Dressingactionsandsymplecticleaves
APoissonactions
BDressingtransformationsandsymplecticleaves
CSymplecticleavesincompactPoisson-Liegroups
DThetwstedease
1.6DeformationofPoissonstructuresandquantization
ADeformationsofPoissonalgebras
BWeylquantization
CQuantizationasdeformation
Bibliographicalnotes

2CoboundaryPoissoI-LiegroupsandtheclassicalYang-Baxterequation
2.1CoboundaryLiebialgebras
ADefinitions
BTheclassicalYang-Baxterequation
CExamples
DTheclassicaldouble
2.2CoboundaryPoisson-Liegroups
ATheSklyaninbracket
Br-matricesand2-cocycles
CTheclassicalR-matrix
23Classicalintegrablesystems
ACompleteintegrability
BLaxpairs
CIntegrablesystemsfromr-matrices
DTodasystems
Bibliographicalnotes

3SolutionsoftheclassicalYang-Baxterequation
3.1ConstantsolutionsoftheCYBE
ATheparameterspaceofnon.skewsolutions
BDescriptionofthesolutions
CExamples
DSkewsolutionsandquasi-FrobeninsLiealgebras
3.2SolutionsoftheCYBEwithspectralparameters
AClnssificationofthesolutions
BEllipticsolutions
CTrigonometriesolutions
DRationalsolutions
Bibliographicalnotes

4QuasitriangularHopfalgebras
4.1Hopfalgebras
ADefinitions
BExamples
CRepresentationsofHopfalgebras
DTopologicalHopfalgebrasandduMity
EIntegrationOllHopfalgebras
FHopf-algebras
4.2QuasitriangularHopfalgebras
AAlmostcocommutativeHopfalgebras
BQuasitriangularHopfalgebras
CRibbonHopfalgebrasandquantumdimension
DThequantumdouble
ETwisting
FSweedler8example
Bibliographicalnotes

5Representationsandquasitensorcategories
5.1Monoidalcategories
AAbeliancategories
BMonoidalcategories
CRigidity
DExamples
EReconstructiontheorems
5.2Quasitensorcategories
ATensorcategories
BQuasitensorcategories
CBalancing
DQuasitensorcategoriesandfusionrules
EQuasitensorcategoriesinquantumfieldtheory
5.3Invariantsofribbontangles
AIsotopyinvariantsandmonoidalfunctors
BTangleinvariants
CCentralek！ments
Bibliographicalnotes

6QuantizationofLiebialgebras
6.1DeformationsofHopfalgebras
ADefmitions
BCohomologytheory
CIugiditytheorems
6.2Quantization
A（Co-）PoissonHopfalgebras
BQuantization
CExistenceofquantizations
6.3Quantizeduniversalenvelopingalgebras
ACocommut&tiveQUEalgebras
BQuasitriangularQUEalgebras
CQUEdualsanddoubles
DThesquareoftheantipode
6.4Thebasicexample
AConstmctmnofthestandardquantization
BAlgebrastructure
CPBWbasis
DQuasitriangularstructure
ERepresentations
FAnon-standardquantization
6.5QuantumKac-Moodyalgebras
AThe-andardquantization
BThecentre
CMultiparameterquantizationsBibliographicalnotes

7Quantizedfunctionalgebras
7.1Thebasicexample
ADefinition
BAbasisof.fn（sL2（c））
CTheR-matrixformulation
DDuality
ERepresentations
7.2R-matrixquantization
AFromIt-matricestobialgebras
BFrombialgebrastoHopfalgebras：thequantumdeterminant
CsolutionsoftheQYBE
7.3Examplesofquantizedfunctionalgebras
AThegeneraldefinition
BThequantumspeciallineargroup
CThequantumorthogonalandsymplecticgroups
DMultiparameterquantizedfunctionalgebras
7.4Differentialcalculusonquantumgroups
AThedeRhamcomplexofthequantumplane
BThedeRhamcomplexofthequantumm×mmatrices
CThedeRhamcomplexofthequantumgenerallineargroup
DInvariantformsonquantumGLm
7.5Integrablelatticemodels
AVertexmodels
BTransfermatrices
……
9SpecializationsofQUEalgebras
10RepresentationsofQUEalgebasthegenericcase
11RepresentationsofQUEalgebastherootofunitycase
12Infinite-dimensionalquantumgroups
13Quantumharmonicanalysis
14Canonicalbases
15Quantumgruopinvariantsfknotsand3-manifolds
16Quasi-HopfalgebrasandtheKnizhnik-Zamolodchikovequation