线性代数群

图书标准信息

• 作者 [美]以弗莱斯 著
• 出版社 世界图书出版公司
• 出版时间 2009-04
• 版次 1
• ISBN 9787510004414
• 定价 28.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 253页
• 正文语种 英语

【内容简介】

Forthisprinting，Ihavecorrectedsomeerrorsandmadenumerousminorchangesintheinterestofclarity.ThemostsignificantcorrectionsoccurinSections4.2，4.3，5.5，30.3，32.1，and32.3.Ihavealsoupdatedthebiblio-graphytosomeextent.Thanksareduetoanumberofreaderswhotookthetroubletopointouterrors，orobscurities;especiallyhelpfulwerethedetailedcommentsofJoseAntonioVargas.

【目录】

I.AlgebraicGeometry
0.SomeCommutativeAlgebra
1.AffineandProjectiveVarieties
1.1IdealsandAflineVarieties
1.2ZariskiTopologyonAffineSpace
1.3IrreducibleComponents
1.4ProductsofAffineVarieties
1.5AffineAlgebrasandMorphisms
1.6ProjectiveVarieties
1.7ProductsofProjectiveVarieties
1.8FlagVarieties

2.Varieties
2.1LocalRings
2.2Prevarieties
2.3Morphisms
2.4Products
2.5HausdorffAxiom

3.Dimension
3.1DimensionofaVariety
3.2DimensionofaSubvariety
3.3DimensionTheorem
3.4Consequences

4.Morphisms
4.1FibresofaMorphism
4.2FiniteMorphisms
4.3ImageofaMorphism
4.4ConstructibleSets
4.5OpenMorphisms
4.6BijectiveMorphisms
4.7BirationalMorphisms

5.TangentSpaces
5.1ZariskiTangentSpace
5.2ExistenceofSimplePoints
5.3LocalRingofaSimplePoint
5.4DifferentialofaMorphism
5.5DifferentialCriterionforSeparability

6.CompleteVarieties
6.1BasicProperties
6.2CompletenessofProjectiveVarieties
6.3VarietiesIsomorphictoP
6.4AutomorphismsofP
II.AflineAlgebraicGroups

7.BasicConceptsandExamples
7.1TheNotionofAlgebraicGroup
7.2SomeClassicalGroups
7.3IdentityComponent
7.4SubgroupsandHomomorphisms
7.5GenerationbyIrreducibleSubsets
7.6HopfAIgebras

8.ActionsofAlgebraicGroupsonVarieties
8.1GroupActions
8.2ActionsofAlgebraicGroups
8.3ClosedOrbits
8.4SemidirectProducts
8.5TranslationofFunctions
8.6LinearizationofAffineGroups
III.LieAlgebras

9.LieAlgebraofanAlgebraicGroup
9.1LieAlgebrasandTangentSpaces
9.2Convolution
9.3Examples
9.4SubgroupsandLieSubalgebras
9.5DualNumbers

10.Differentiation
10.1SomeElementaryFormulas
10.2DifferentialofRightTranslation
10.3TheAdjointRepresentation
10.4DifferentialofAd
10.5Commutators
10.6Centralizers
10.7AutomorphismsandDerivations
IV.HomogeneousSpaces

11.ConstructionofCertainRepresentations
11.1ActiononExteriorPowers
11.2ATheoremofChevalley
11.3PassagetoProjectiveSpace
11.4CharactersandSemi-lnvariants
11.5NormalSubgroups

12.Quotients
12.1UniversalMappingProperty
12.2TopologyofY
12.3FunctionsonY
12.4Complements
12.5Characteristic0
V.Characteristic0Theory

13.CorrespondenceBetweenGroupsandLieAlgebras
13.1TheLatticeCorrespondence
13.2InvariantsandInvariantSubspaces
13.3NormalSubgroupsandIdeals
13.4CentersandCentralizers
13.5SemisimpleGroupsandLieAlgebras

14.SemisimpleGroups
14.1TheAdjointRepresentation
14.2SubgroupsoraSemisimpleGroup
14.3CompleteReducibilityofRepresentations
VI.SemisimpleandUnipotentElements

15.Jordan-ChevalleyDecomposition
15.1DecompositionofaSingleEndomorphism
15.2GL（n，K）andgl（n，K）
15.3JordanDecompositioninAlgebraicGroups
15.4CommutingSetsofEndomorphisms
15.5StructureofCommutativeAlgebraicGroups

16.DiagonalizableGroups
16.1Charactersandd-Groups
16.2Tori
16.3RigidityofDiagonalizableGroups
16.4WeightsandRoots
VII.SolvableGroups

17.NilpotentandSolvableGroups
17.1AGroup-TheoreticLemma
17.2CommutatorGroups
17.3SolvableGroups
17.4NilpotentGroups
17.5UnipotentGroups
17.6Lie-KolchinTheorem

18.SemisimpleElements
18.1GlobalandInfinitesimalCentralizers
18.2ClosedConjugacyClasses
18.3ActionofaSemisimpleElementonaUnipotentGroup
18.4ActionofaDiagonalizableGroup

19.ConnectedSolvableGroups
19.1AnExactSequence
19.2TheNilpotentCase
19.3TheGeneralCase
19.4NormalizerandCentralizer
19.5SolvableandUnipotentRadicals

20.OneDimensionalGroups
20.1CommutativityofG
20.2VectorGroupsande-Groups
20.3Propertiesofp-Polynomials
20.4AutomorphismsofVectorGroups
20.5TheMainTheorem
VIII.BorelSubgroups

21.FixedPointandConjugacyTheorems
21.1ReviewofCompleteVarieties
21.2FixedPointTheorem
21.3ConjugacyofBorelSubgroupsandMaximalTori
21.4FurtherConsequences

22.DensityandConnectednessTheorems
22.1TheMainLemma
22.2DensityTheorem
22.3ConnectednessTheorem
22.4BorelSubgroupsofCG（S）
22.5CartanSubgroups：Summary

23.NormalizerTheorem
23.1StatementoftheTheorem
23.2ProofoftheTheorem
23.3TheVarietyG/B
23.4Summary
IX.CentralizersofTori

24.RegularandSingularTori
24.1WeylGroups
24.2RegularTori
24.3SingularToriandRoots
24.4Regular1-ParameterSubgroups

25.ActionofaMaximalTorusonG/B
25.1Actionofa1-ParameterSubgroup
25.2ExistenceofEnoughFixedPoints
25.3GroupsofSemisimpleRank1
25.4WeylChambers

26.TheUnipotentRadical
26.1CharacterizationofRu（G）
26.2SomeConsequences
26.3TheGroupsUa
X.StructureofReductiveGroups

27.TheRootSystem
27.1AbstractRootSystems
27.2TheIntegralityAxiom
27.3SimpleRoots
27.4TheAutomorphismGroupofaSemisimpleGroup
27.5SimpleComponents

28.BruhatDecomposition
28.1T-StableSubgroupsofBu
28.2GroupsofSemisimpleRank1
28.3TheBruhatDecomposition
28.4NormalForminG
28.5Complements

29.TitsSystems
29.1Axioms
29.2BruhatDecomposition
29.3ParabolicSubgroups
29.4GeneratorsandRelationsforW
29.5NormalSubgroupsofG

30.ParabolicSubgroups
30.1StandardParabolicSubgroups
30.2LeviDecompositions
30.3ParabolicSubgroupsAssociatedtoCertainUnipotentGroups
30.4MaximalSubgroupsandMaximalUnipotentSubgroups
XI.RepresentationsandClassificationofSemisimpleGroups

31.Representations
31.1Weights
31.2MaximalVectors
31.3IrreducibleRepresentations
31.4ConstructionofIrreducibleRepresentations
31.5MultiplicitiesandMinimalHighestWeights
31.6ContragredientsandInvariantBilinearForms

32.IsomorphismTheorem
32.1TheClassificationProblem
32.2ExtensionofψTtoN（T）
32.3ExtensionofψTtoZa
32.4ExtensionofψTtoTUa
32.5ExtensionofψTtoB
32.6Multiplicativityofψ

33.RootSystemsofRank2
33.1Reformulationof（A），（B），（C）
33.2SomePreliminaries
33.3TypeA2
33.4TypeB2
33.5TypeG2
33.6TheExistenceProblem
XII.SurveyofRationalityProperties

34.FieldsofDefinition
34.1Foundations
34.2ReviewofEarlierChapters
34.3Tori
34.4SomeBasicTheorems
34.5Borei-TitsStructureTheory
34.6AnExample：OrthogonalGroups

35.SpecialCases
35.1SplitandQuasisplitGroups
35.2FiniteFields
35.3TheRealField
35.4LocalFields
35.5Classification
Appendix.RootSystems
Bibliography
IndexofTerminology
IndexofSymbols