线性代数群
线性代数群封面图

线性代数群

(美) 汉弗莱斯 (Humphreys,J.E.) , 著

出版社:世界图书出版公司北京公司

年代:2009

定价:28.0

书籍简介:

本书是线性代数群的基本著作,它是以作者于1969年和1971~1972年在几所学校讲课的讲义为基础形成的。初版于1975年,本书于1998年第五次修订重印本,介绍了任意特征代数闭域K上的有关理论。全书论述清晰,易于入门。

书籍目录:

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

Ⅴ.CharacteristicOTheory

Ⅵ.SemisimpleandUnipotentElements

Ⅶ.SolvableGroups

Ⅷ.BorelSubgroups

Ⅸ.CentralizersofTori

Ⅹ.StructureofReductiveGroups

Ⅺ.RepresentatinsandClassficationofSemisimpleGroups

Ⅻ.SurveyofRationalityProperties

AppendixRootSystems

Bibliography

IndexofTerminology

IndexofSymbols

内容摘要:

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

书籍规格:

书籍详细信息
书名线性代数群站内查询相似图书
9787510004414
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出版地北京出版单位世界图书出版公司北京公司
版次1版印次1
定价(元)28.0语种英文
尺寸14装帧平装
页数印数 2000

书籍信息归属:

线性代数群是世界图书出版公司北京公司于2009.04出版的中图分类号为 O187.2 的主题关于 线性代数群-英文 的书籍。