"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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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
装帧精装
上书时间2024-05-29
商品详情
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图书标准信息
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作者
[俄罗斯]帕尔申 著
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出版社
科学出版社
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出版时间
2009-01
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版次
1
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ISBN
9787030234889
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定价
68.00元
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装帧
精装
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开本
16开
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纸张
胶版纸
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页数
284页
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字数
358千字
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正文语种
英语
- 【内容简介】
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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.
- 【目录】
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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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