• 线性代数群(第2版)(英文版)
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线性代数群(第2版)(英文版)

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作者[美]布罗尔 著

出版社世界图书出版公司

出版时间2009-08

版次1

装帧平装

货号C27-47

上书时间2024-11-03

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图书标准信息
  • 作者 [美]布罗尔 著
  • 出版社 世界图书出版公司
  • 出版时间 2009-08
  • 版次 1
  • ISBN 9787510004810
  • 定价 38.00元
  • 装帧 平装
  • 开本 24开
  • 纸张 胶版纸
  • 页数 288页
  • 正文语种 英语
【内容简介】
  ApartfromsomeknowledgeofLiealgebras,themainprerequisitefortheseNotesissomefamiliaritywithalgebraicgeometry.Infact,comparativelylittleisactuallyneeded.MostofthenotionsandresultsfrequentlyusedintheNotesaresummarized,afewwithproofs,inapreliminaryChapterAG.Asabasicreference,wetakeMumfordsNotes[14],andhavetriedtobetosomeextentself-containedfromthere.Afewfurtherresultsfromalgebraicgeometryneededonsomespecificoccasionswillberecalled(withreferences)whereused.Thepointofviewadoptedhereisessentiallythesettheoreticone:varietiesareidentifiedwiththeirsetofpointsoveranalgebraicclosureofthegroundfield(endowedwiththeZariski-topology),howeverwithsometracesoftheschemepointofviewhereandthere.
【目录】
IntroductiontotheFirstEdition
IntroductiontotheSecondEdition
ConventionsandNotation
CHAPTERAG--BackgroundMaterialFromAlgebraicGeometry
1.SomeTopologicalNotions
2.SomeFactsfromFieldTheory
3.SomeCommutativeAlgebra
4.Sheaves
5.AffineK-Schemes,Prevarieties
6.Products;Varieties
7.ProjectiveandCompleteVarieties
8.RationalFunctions;DominantMorphisms
9.Dimension
10.ImagesandFibresofaMorphism
11.k-structuresonK-Schemes
12.k-StructuresonVarieties
13.Separablepoints
14.GaloisCriteriaforRationality
15.DerivationsandDifferentials
16.TangentSpaces
17.SimplePoints
18.NormalVarieties
References
CHAPTERI--GeneralNotionsAssociatedWithAlgebraicGroups
1.TheNotionofanAlgebraicGroups
2.GroupClosure;SolvableandNilpotentGroups
3.TheLieAlgebraofanAlgebraicGroup
4.JordanDecomposition
CHAPTER11HomogeneousSpaces
5.Semi-lnvariants
6.HomogeneousSpaces
7.AlgebraicGroupsinCharacteristicZero
CHAPTER111SolvableGroups
8.DiagonalizableGroupsandTori
9.ConjugacyClassesandCentralizersofScmi-SimpleElements
10.ConnectedSolvableGroups
CHAPTERIV--BorelSubgroups;RcductiveGroups
11.BoreiSubgroups
12.CaftanSubgroups;RegularElements
13.TheBorelSubgroupsContainingaGivenTorus
14.RootSystemsandBruhatDecompositioninReductiveGroups
CHAPTERV--RationalityQuestions
15.SplitSolvableGroupsandSubgroups
16.GroupsoverFiniteFields
17.QuotientofaGroupbyaLieSubalgebra
18.CartanSubgroupsovertheGroundfield.Unirationality.SplittingofReductiveGroups
19.CartanSubgroupsofSolvableGroups
20.lsotropicReductiveGroups
21.RelativeRootSystemandBruhatDecompositionforlsotropicReductiveGroups
22.Centrallsogenies
23.Examples
24.SurveyofSomeOtherTopics
A.Classification
B.LinearRepresentations
C.RealReductiveGroups
ReferencesforChaptersItoV
IndexofDefinition
IndexofNotation
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