图书信息

作者简介

内容简介

目录

图书信息

出版社: 世界图书出版公司; 第1版 (2009年4月1日)

外文书名: Linear Algebraic Groups

平装: 253页

正文语种: 英语

开本: 24

ISBN: 9787510004414, 7510004411

条形码: 9787510004414

尺寸: 22 x 14.8 x 1.2 cm

重量: 340 g

作者简介

作者：(美国) 汉弗莱斯 (Humphreys.J.E.)

内容简介

《线性代数群》讲述了：For this printing, I have corrected some errors and made numerous minor changes in the interest of clarity. The most significant corrections occur in Sections 4.2, 4.3, 5.5, 30.3, 32.1, and 32.3. I have also updated the biblio-graphy to some extent. Thanks are due to a number of readers who took the trouble to point out errors, or obscurities; especially helpful were the detailed comments of Jose Antonio Vargas...

目录

I.AlgebraicGeometry

0.SomeCommutativeAlgebra

1.AffineandProjectiveVarieties

1.1 IdealsandAflineVarieties

1.2 ZariskiTopologyonAffineSpace

1.3 IrreducibleComponents

1.4 ProductsofAffineVarieties

1.5 AffineAlgebrasandMorphisms

1.6 ProjectiveVarieties

1.7 ProductsofProjectiveVarieties

1.8 FlagVarieties

2.Varieties

2.1 LocalRings

2.2 Prevarieties

2.3 Morphisms

2.4 Products

2.5 HausdorffAxiom

3.Dimension

3.1 DimensionofaVariety

3.2 DimensionofaSubvariety

3.3 DimensionTheorem

3.4 Consequences

4.Morphisms

4.1 FibresofaMorphism

4.2 FiniteMorphisms

4.3 ImageofaMorphism

4.4 ConstructibleSets

4.5 OpenMorphisms

4.6 BijectiveMorphisms

4.7 BirationalMorphisms

5.TangentSpaces

5.1 ZariskiTangentSpace

5.2 ExistenceofSimplePoints

5.3 LocalRingofaSimplePoint

5.4 DifferentialofaMorphism

5.5 DifferentialCriterionforSeparability

6.CompleteVarieties

6.1 BasicProperties

6.2 CompletenessofProjectiveVarieties

6.3 VarietiesIsomorphictoP

6.4 AutomorphismsofP

II.AflineAlgebraicGroups

7.BasicConceptsandExamples

7.1 TheNotionofAlgebraicGroup

7.2 SomeClassicalGroups

7.3 IdentityComponent

7.4 SubgroupsandHomomorphisms

7.5 GenerationbyIrreducibleSubsets

7.6 HopfAIgebras

8.ActionsofAlgebraicGroupsonVarieties

8.1 GroupActions

8.2 ActionsofAlgebraicGroups

8.3 ClosedOrbits

8.4 SemidirectProducts

8.5 TranslationofFunctions

8.6 LinearizationofAffineGroups

III.LieAlgebras

9.LieAlgebraofanAlgebraicGroup

9.1 LieAlgebrasandTangentSpaces

9.2 Convolution

9.3 Examples

9.4 SubgroupsandLieSubalgebras

9.5 DualNumbers

10.Differentiation

10.1 SomeElementaryFormulas

10.2 DifferentialofRightTranslation

10.3 TheAdjointRepresentation

10.4 DifferentialofAd

10.5 Commutators

10.6 Centralizers

10.7 AutomorphismsandDerivations

IV.HomogeneousSpaces

11.ConstructionofCertainRepresentations

11.1 ActiononExteriorPowers

11.2 ATheoremofChevalley

11.3 PassagetoProjectiveSpace

11.4 CharactersandSemi-lnvariants

11.5 NormalSubgroups

12.Quotients

12.1 UniversalMappingProperty

12.2 TopologyofY

12.3 FunctionsonY

12.4 Complements

12.5 Characteristic0

V.Characteristic0Theory

13.CorrespondenceBetweenGroupsandLieAlgebras

13.1 TheLatticeCorrespondence

13.2 InvariantsandInvariantSubspaces

13.3 NormalSubgroupsandIdeals

13.4 CentersandCentralizers

13.5 SemisimpleGroupsandLieAlgebras

14.SemisimpleGroups

14.1 TheAdjointRepresentation

14.2 SubgroupsoraSemisimpleGroup

14.3 CompleteReducibilityofRepresentations

VI.SemisimpleandUnipotentElements

15.Jordan-ChevalleyDecomposition

15.1 DecompositionofaSingleEndomorphism

15.2 GL(n,K)andgl(n,K)

15.3 JordanDecompositioninAlgebraicGroups

15.4 CommutingSetsofEndomorphisms

15.5 StructureofCommutativeAlgebraicGroups

16.DiagonalizableGroups

16.1 Charactersandd-Groups

16.2 Tori

16.3 RigidityofDiagonalizableGroups

16.4 WeightsandRoots

VII.SolvableGroups

17.NilpotentandSolvableGroups

17.1 AGroup-TheoreticLemma

17.2 CommutatorGroups

17.3 SolvableGroups

17.4 NilpotentGroups

17.5 UnipotentGroups

17.6 Lie-KolchinTheorem

18.SemisimpleElements

18.1 GlobalandInfinitesimalCentralizers

18.2 ClosedConjugacyClasses

18.3 ActionofaSemisimpleElementonaUnipotentGroup

18.4 ActionofaDiagonalizableGroup

19.ConnectedSolvableGroups

19.1 AnExactSequence

19.2 TheNilpotentCase

19.3 TheGeneralCase

19.4 NormalizerandCentralizer

19.5 SolvableandUnipotentRadicals

20.OneDimensionalGroups

20.1 CommutativityofG

20.2 VectorGroupsande-Groups

20.3 Propertiesofp-Polynomials

20.4 AutomorphismsofVectorGroups

20.5 TheMainTheorem

VIII.BorelSubgroups

21.FixedPointandConjugacyTheorems

21.1 ReviewofCompleteVarieties

21.2 FixedPointTheorem

21.3 ConjugacyofBorelSubgroupsandMaximalTori

21.4 FurtherConsequences

22.DensityandConnectednessTheorems

22.1 TheMainLemma

22.2 DensityTheorem

22.3 ConnectednessTheorem

22.4 BorelSubgroupsofCG(S)

22.5 CartanSubgroups:Summary

23.NormalizerTheorem

23.1 StatementoftheTheorem

23.2 ProofoftheTheorem

23.3 TheVarietyG/B

23.4 Summary

IX.CentralizersofTori

24.RegularandSingularTori

24.1 WeylGroups

24.2 RegularTori

24.3 SingularToriandRoots

24.4 Regular1-ParameterSubgroups

25.ActionofaMaximalTorusonG/B

25.1 Actionofa1-ParameterSubgroup

25.2 ExistenceofEnoughFixedPoints

25.3 GroupsofSemisimpleRank1

25.4 WeylChambers

26.TheUnipotentRadical

26.1 CharacterizationofRu(G)

26.2 SomeConsequences

26.3 TheGroupsUa

X.StructureofReductiveGroups

27.TheRootSystem

27.1 AbstractRootSystems

27.2 TheIntegralityAxiom

27.3 SimpleRoots

27.4 TheAutomorphismGroupofaSemisimpleGroup

27.5 SimpleComponents

28.BruhatDecomposition

28.1 T-StableSubgroupsofBu

28.2 GroupsofSemisimpleRank1

28.3 TheBruhatDecomposition

28.4 NormalForminG

28.5 Complements

29.TitsSystems

29.1 Axioms

29.2 BruhatDecomposition

29.3 ParabolicSubgroups

29.4 GeneratorsandRelationsforW

29.5 NormalSubgroupsofG

30.ParabolicSubgroups

30.1 StandardParabolicSubgroups

30.2 LeviDecompositions

30.3 ParabolicSubgroupsAssociatedtoCertainUnipotentGroups

30.4 MaximalSubgroupsandMaximalUnipotentSubgroups

XI.RepresentationsandClassificationofSemisimpleGroups

31.Representations

31.1 Weights

31.2 MaximalVectors

31.3 IrreducibleRepresentations

31.4 ConstructionofIrreducibleRepresentations

31.5 MultiplicitiesandMinimalHighestWeights

31.6 ContragredientsandInvariantBilinearForms

32.IsomorphismTheorem

32.1 TheClassificationProblem

32.2 ExtensionofψTtoN(T)

32.3 ExtensionofψTtoZa

32.4 ExtensionofψTtoTUa

32.5 ExtensionofψTtoB

32.6 Multiplicativityofψ

33.RootSystemsofRank2

33.1 Reformulationof(A),(B),(C)

33.2 SomePreliminaries

33.3 TypeA2

33.4 TypeB2

33.5 TypeG2

33.6 TheExistenceProblem

XII.SurveyofRationalityProperties

34.FieldsofDefinition

34.1 Foundations

34.2 ReviewofEarlierChapters

34.3 Tori

34.4 SomeBasicTheorems

34.5 Borei-TitsStructureTheory

34.6 AnExample:OrthogonalGroups

35.SpecialCases

35.1 SplitandQuasisplitGroups

35.2 FiniteFields

35.3 TheRealField

35.4 LocalFields

35.5 Classification

Appendix.RootSystems

Bibliography

IndexofTerminology

IndexofSymbols