霍普夫代数

图书标准信息

• 作者 [日]英一安倍晋三 著
• 出版社 世界图书出版公司
• 出版时间 2009-05
• 版次 1
• ISBN 9787510004568
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 284页
• 正文语种 英语

【内容简介】

Ifforinstance，wereplacethefinitegroupGintheaboveargumentbyatopologicalgroupandkbythefieldofrealnumbersorthefieldofcomplexnumbers，orifwetakeGtobeanalgebraicgroupoveranalgebraicallyclosedfieldkandAisreplacedbythek-algebraofallcontinuousrepresentativefunctionsorofallregularfunctionsoverG，thenAturnsouttobeak-Hopfalgebrainexactlythesamemanner.ThesealgebraicsystemsplayanimportantrolewhenstudyingthestructureofG.Similarly，ak-Hopfalgebrastructurecanbedefinednaturallyontheuniversalenvelopingalgebraofak-Liealgebra.TheuniversalenvelopingalgebraoftheLiealgebraofasemi-simplealgebraicgroupturnsouttobe（inasense）thedualoftheHopfalgebradefinedabove.TheseconstitutesomeofthemostnaturalexamplesofHopfalgebras.Thegeneralstructureofsuchalgebraicsystemshasrecentlybecomeafocusofinterestincon-junctionwithitsapplicationstothetheoryofalgebraicgroupsortheGaloistheoryofpurelyinseparableextensions，andagreatdealofresearchiscurrentlybeingconductedinthisarea.

【目录】

Preface
Notation
1Modulesandalgebras
1．Modules
2．Algebrasoveracommutativering
3．Liealgebras
4．Semi-simplealgebras
5．Finitelygeneratedcommutativealgebras
2Hopfalgebras
1．BialgcbrasandHopfalgebras
2．Therepresentativebialgebrasofsemigroups
3．Thedualitybetweenalgebrasandcoalgebras
4．Irreduciblebialgebras
5．IrreduciblecocommutativebiaIgebras
3Hopralgebrasandrelnmmamtlomofgroup
1．Comodulesandbimodules
2．BimodulesandbiaIgebms
3．IntegralsforHopfalgebras
4．Thedualitytheorem
4ApplimlJonstoalgebraicgroups
1．Affmek-varieties
2．Atonek-groups
3．Liealgebrasofaffmealgebraick-groups
4．Factorgroups
5．Unipotentgroupsandsolvablegroups
6．Completelyreduciblegroups
5Applicationstofieldtheory
1．K／k—bialgebras
2．Jacobson'stheorem
3．Modularextensions
Appendix：Categoriesandfunctors
A．1Categories
A．2Functors
A．3Adjointfunctors
A．4Representablefunctors
A．5φ-groupsandφ-cogroups
References
Index