"国外数学名著系列（续一）（影印版）45：代数几何4（线性代数群不变量理论（影印版））"

作者: [俄罗斯] 帕尔申著

出版社: 科学出版社

出版时间: 2009-01

版次: 1

ISBN: 9787030234889

定价: 68.00

装帧: 精装

开本: 16开

纸张: 胶版纸

页数: 284页

字数: 358千字

正文语种: 英语

分类: 自然科学

1 张插图图片

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　　Thisbookcontainstwocontributionsoncloselyrelatedsubjects：thetheoryoflinearalgebraicgroupsandinvarianttheory.ThefirstpartiswrittenbyT.A.Springer,awell-knownexpertinthefirstmentionedfield.Hcpresentsacomprehensivesurvey,whichcontainsnumeroussketchedproofsandhediscussestheparticularfeaturesofalgebraicgroupsoverspecialfields(finite,local,andglobal).Theauthorsofparttwo-E.B.VinbcrgandV.L.Popov-arcamongthemostactiveresearchersininvarianttheory.Thelast20yearshavebccnaperiodofvigorousdevelopmentinthisfieldductotheinfluenceofmodernmethodsfromalgebraicgeometry.Thebookwillbcveryusefulasareferenceandresearchguidetograduatestudentsandresearchersinmathematicsandtheoreticalphysics. I.LinearalgebraicGroups
Introduction
HistoricalComments
Chapter1.LinearAlgebraicGroupsoveranAlgebraically
1.RecollectionsfromAlgebraicGeometry
1.1.AffineVarieties
1.2.Morphisms
1.3.SomeTopologicalProperties
1.4.TangentSpaces
1.5.PropertiesofMorphisms
1.6.Non-AffineVarieties

2.LinearAlgebraicGroups，BasicDefinitionsandProperties
2.1.TheDefinitionofaLinearAlgebraicGroup
2.2.SomeBasicFacts
2.3.G-Spaces
2.4.TheLieAlgebraofanAlgebraicGroup
2.5.Quotients

3.StructuralPropertiesofLinearAlgebraicGroups
3.1.JordanDecompositionandRelatedResults
3.2.DiagonalizableGroupsandTori
3.3.One-DimensionalConnectedGroups
3.4.ConnectedSolvableGroups
3.5.ParabolicSubgroupsandBorelSubgroups
3.6.Radicals，Semi-simpleandReductiveGroups

4.ReductiveGroups
4.1.GroupsofRankOne
4.2.TheRootDatumandtheRootSystem
4.3.BasicPropertiesofReductiveGroups
4.4.ExistenceandUniquenessTheoremsforReductiveGroups
4.5.ClassificationofQuasi-simpleLinearAlgebraicGroups
4.6.RepresentationTheory

Chapter2.LinearAlgebraicGroupsoverArbitraryGroundFields
1.RecollectionsfromAlgebraicGeometry
1.1.F-StructuresonAffineVarieties
1.2.F-StructuresonArbitraryVarieties
1.3.Forms
1.4.RestrictionoftheGroundField

2.F-Groups，BasicProperties
2.1.GeneralitiesAboutF-Groups
2.2.Quotients
2.3.Forms
2.4.RestrictionoftheGroundField

3.Tori
3.1.F-Tori
3.2.F-ToriinF-Groups
3.3.SplitToriinF-Groups

4.SolvableGroups
4.1.SolvableGroups
4.2.Sections
4.3.ElementaryUnipotentGroups
4.4.PropertiesofSplitSolvableGroups
4.5.BasicResultsAboutSolvableF-Groups

5.ReductiveGroups
5.1.SplitReductiveGroups
5.2.ParabolicSubgroups
5.3.TheSmallRootSystem
5.4.TheGroupsG(F)
5.5.TheSphericalTitsBuildingofaReductiveF-Group

6.ClassificationofReductiveF-Groups
6.1.IsomorphismTheorem
6.2.Existence
6.3.RepresentationTheoryofF-Groups

Chapter3.SpecialFields
1.LieAlgebrasofAlgebraicGroupsinCharacteristicZero
1.1.AlgebraicSubalgebras

2.AlgebraicGroupsandLieGroups
2.1.LocallyCompactFields
2.2.RealLieGroups

3.LinearAlgebraicGroupsoverFiniteFields
3.1.LangsTheoremanditsConsequences
3.2.FiniteGroupsofLieType
3.3.RepresentationsofFiniteGroupsofLieType

4.LinearAlgebraicGroupsoverFieldswithaValuation
4.1.TheApartmentandAffineDynkinDiagram
4.2.TheAffineBuilding
4.3.TitsSystem，Decompositions
4.4.LocalFields

5.GlobalFields
5.1.AdeleGroups
5.2.ReductionTheory
5.3.FinitenessResults
5.4.GaloisCohomology
References
II.InvariantTheory
AutborIndex
SubjectIndex
内容简介:
　　Thisbookcontainstwocontributionsoncloselyrelatedsubjects：thetheoryoflinearalgebraicgroupsandinvarianttheory.ThefirstpartiswrittenbyT.A.Springer,awell-knownexpertinthefirstmentionedfield.Hcpresentsacomprehensivesurvey,whichcontainsnumeroussketchedproofsandhediscussestheparticularfeaturesofalgebraicgroupsoverspecialfields(finite,local,andglobal).Theauthorsofparttwo-E.B.VinbcrgandV.L.Popov-arcamongthemostactiveresearchersininvarianttheory.Thelast20yearshavebccnaperiodofvigorousdevelopmentinthisfieldductotheinfluenceofmodernmethodsfromalgebraicgeometry.Thebookwillbcveryusefulasareferenceandresearchguidetograduatestudentsandresearchersinmathematicsandtheoreticalphysics.
目录:
I.LinearalgebraicGroups
Introduction
HistoricalComments
Chapter1.LinearAlgebraicGroupsoveranAlgebraically
1.RecollectionsfromAlgebraicGeometry
1.1.AffineVarieties
1.2.Morphisms
1.3.SomeTopologicalProperties
1.4.TangentSpaces
1.5.PropertiesofMorphisms
1.6.Non-AffineVarieties

2.LinearAlgebraicGroups，BasicDefinitionsandProperties
2.1.TheDefinitionofaLinearAlgebraicGroup
2.2.SomeBasicFacts
2.3.G-Spaces
2.4.TheLieAlgebraofanAlgebraicGroup
2.5.Quotients

3.StructuralPropertiesofLinearAlgebraicGroups
3.1.JordanDecompositionandRelatedResults
3.2.DiagonalizableGroupsandTori
3.3.One-DimensionalConnectedGroups
3.4.ConnectedSolvableGroups
3.5.ParabolicSubgroupsandBorelSubgroups
3.6.Radicals，Semi-simpleandReductiveGroups

4.ReductiveGroups
4.1.GroupsofRankOne
4.2.TheRootDatumandtheRootSystem
4.3.BasicPropertiesofReductiveGroups
4.4.ExistenceandUniquenessTheoremsforReductiveGroups
4.5.ClassificationofQuasi-simpleLinearAlgebraicGroups
4.6.RepresentationTheory

Chapter2.LinearAlgebraicGroupsoverArbitraryGroundFields
1.RecollectionsfromAlgebraicGeometry
1.1.F-StructuresonAffineVarieties
1.2.F-StructuresonArbitraryVarieties
1.3.Forms
1.4.RestrictionoftheGroundField

2.F-Groups，BasicProperties
2.1.GeneralitiesAboutF-Groups
2.2.Quotients
2.3.Forms
2.4.RestrictionoftheGroundField

3.Tori
3.1.F-Tori
3.2.F-ToriinF-Groups
3.3.SplitToriinF-Groups

4.SolvableGroups
4.1.SolvableGroups
4.2.Sections
4.3.ElementaryUnipotentGroups
4.4.PropertiesofSplitSolvableGroups
4.5.BasicResultsAboutSolvableF-Groups

5.ReductiveGroups
5.1.SplitReductiveGroups
5.2.ParabolicSubgroups
5.3.TheSmallRootSystem
5.4.TheGroupsG(F)
5.5.TheSphericalTitsBuildingofaReductiveF-Group

6.ClassificationofReductiveF-Groups
6.1.IsomorphismTheorem
6.2.Existence
6.3.RepresentationTheoryofF-Groups

Chapter3.SpecialFields
1.LieAlgebrasofAlgebraicGroupsinCharacteristicZero
1.1.AlgebraicSubalgebras

2.AlgebraicGroupsandLieGroups
2.1.LocallyCompactFields
2.2.RealLieGroups

3.LinearAlgebraicGroupsoverFiniteFields
3.1.LangsTheoremanditsConsequences
3.2.FiniteGroupsofLieType
3.3.RepresentationsofFiniteGroupsofLieType

4.LinearAlgebraicGroupsoverFieldswithaValuation
4.1.TheApartmentandAffineDynkinDiagram
4.2.TheAffineBuilding
4.3.TitsSystem，Decompositions
4.4.LocalFields

5.GlobalFields
5.1.AdeleGroups
5.2.ReductionTheory
5.3.FinitenessResults
5.4.GaloisCohomology
References
II.InvariantTheory
AutborIndex
SubjectIndex

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"国外数学名著系列（续一）（影印版）45：代数几何4（线性代数群不变量理论（影印版））"

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