线性代数群（第2版）（英文版）

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