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
商品详情
- 品相描述:全新
图书标准信息
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作者
[美]布罗尔 著
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出版社
世界图书出版公司
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出版时间
2009-08
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版次
1
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ISBN
9787510004810
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定价
38.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
288页
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正文语种
英语
- 【内容简介】
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ApartfromsomeknowledgeofLiealgebras,themainprerequisitefortheseNotesissomefamiliaritywithalgebraicgeometry.Infact,comparativelylittleisactuallyneeded.MostofthenotionsandresultsfrequentlyusedintheNotesaresummarized,afewwithproofs,inapreliminaryChapterAG.Asabasicreference,wetakeMumfordsNotes[14],andhavetriedtobetosomeextentself-containedfromthere.Afewfurtherresultsfromalgebraicgeometryneededonsomespecificoccasionswillberecalled(withreferences)whereused.Thepointofviewadoptedhereisessentiallythesettheoreticone:varietiesareidentifiedwiththeirsetofpointsoveranalgebraicclosureofthegroundfield(endowedwiththeZariski-topology),howeverwithsometracesoftheschemepointofviewhereandthere.
- 【目录】
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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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