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| 內容簡介： |
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Thisvolumeisacompletelynewversionofthebookunderthesametitle，whichappearedin1981asVolume9intheseries"ProgressinMathematics，"andwhichhasbeenoutofprintforsometime.Thatbookhaditsorigininnotes（takenbyHassanAzad）fromacourseonthetheoryofLinearalgebraicgroups，givenattheUniversityofNotreDameinthefallof1978.Theaimofthebookwastopresentthetheoryoflinearalgebraicgroupsoveranalgebraicallyclosedfield，includingthebasicresultsonreductivegroups.Adistinguishingfeaturewasaself-containedtreatmentoftheprerequisitesfromalgebraicgeometryandcommutativealgebra.
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| 目錄：
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PrefacetotheSecondEdition
1.SomeAlgebraicGeometry
1.1.TheZariskitopology
1.2.lrreducibilityoftopologicalspaces
1.3.Affinealgebras
1.4.Regularfunctions,ringedspaces
1.5.Products
1.6.Prevarietiesandvarieties
1.7.Projectivevarieties
1.8.Dimension
1.9.Someresultsonmorphisms
Notes
2.LinearAlgebraicGroups,FirstProperties
2.1.Algebraicgroups
2.2.Somebasicresults
2.3.G-spaces
2.4.Jordandecomposition
2.5.Recoveringagroupfromitsrepresentations
Notes
3.CommutativeAlgebraicGroups
3.1.Structureofcommutativealgebraicgroups
3.2.Diagonalizablegroupsandtori
3.3.Additivefunctions
3.4.Elementaryunipotentgroups
Notes
4.Demrations,DiffeRntials,LieAlgebras
4.1.Derivationsandtangentspaces
4.2.Differentials,separability
4.3.Simplepoints
4.4.TheLiealgebraofalinearalgebraicgroup
Notes
5.TopologicalPropertiesofMorphisms,Applications
5.1.Topologicalpropertiesofmorphisms
5.2.Fjnitemorphisms,normality
5.3.Homogeneousspaces
5.4.Semi-simpleautomorphisms
5.5.Quotients
Notes
6.ParabolicSubgroups,BorelSubgoupsSolvableGroups
6.1.Completevarieties
6.2.ParabolicsubgroupsandBorclsubgroups
6.3.Connectedsolvablegroups
6.4.Maximaltori,furtherpropertiesofBorelgroups
Notes
7.WeylGroup,Roots,RootDatum
8.ReductiveGroups
9.TheIsomorphismTheorem
10.TheExistenceTheorem
11.MoreAlgebraicGeometry
12.F-groups:GeneralResults
13.F-tori
14.SolvableF-groups
15.F_reductiveGroups
16.RedoctiveF-groups
17.Classification
TableofIndices
Bibliography
Index
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