经典数学丛书（影印版）：李代数和代数群

图书标准信息

• 作者 [法]陶威尔（Tauvel P.） 著
• 出版社 世界图书出版公司
• 出版时间 2014-03
• 版次 1
• ISBN 9787510070228
• 定价 99.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 653页
• 正文语种 英语

【内容简介】

　　ThetheoryofgroupsandLiealgebrasisinterestingformanyreasons.Inthemathematicalviewpoint，itemploysatthesametimealgebra，analysisandgeometry.Ontheotherhand，itintervenesinotherareasofscience，inparticularindifferentbranchesofphysic8andchemistry.Itisanactivedomainofcurrentresearch.
　　Thegeneraltheoryofalgebraicgroupsisstudiedinchapter821to28.TherelationsbetweenLiealgebrasandalgebraicgroups，whicharefundamentaltous，areestablishedinchapters23and24.Chapter29present8applicationsoftheserelationstotacklethesystematicstudyofLiealgebras.Thereaderwillobservethatthegeometricalaspectshaveanimportantpartinthisstudy.Inparticular，theorbitsofpointsundertheactionofanalgebraicgroupplaysacentralrole.

【目录】

1Resultsontopologicalspaces
1.1Irreduciblesetsandspaces
1.2Dimension
1.3Noetherianspaces
1.4Constructiblesets
1.5Gluingtopologicalspaces

2Ring8andmodules
2.1Ideals
2.2Primeandmaximalideals
2.3Ringsoffractionsandlocalization
2.4Localizationsofmodules
2.5Radicalofanideal
2.6Localrings
2.7Noetherianringsandmodules
2.8Derivations
2.9Moduleofdifferentials

3Integralextensions
3.1Integraldependence
3.2Integrallycloseddomains
3.3Extensionsofprimeideals

4Factorialrings
4.1Generalities
4.2Uniquefactorization
4.3PrincipalidealdomainsandEuclideandomains
4.4Polynomialsandfactorialrings
4.5Symmetricpolynomials
4.6Resultantanddiscriminant

5Fieldextensions
5.1Extensions
5.2Algebraicandtranscendentalelements
5.3Algebraicextensions
5.4Transcendencebasis
5.5Normandtrace
5.6Theoremoftheprimitiveelement
5.7GoingDownTheorem
5.8Fieldsandderivations
5.9Conductor

6Finitelygeneratedalgebras
6.1Dimension
6.2Noether'sNormalizationTheorem
6.3Krull'sPrincipalIdealTheorem*
6.4Maximalideals
6.5Zariskitopology

7Gradingsandfiltrations
7.1Gradedringsandgradedmodules
7.2Gradedsubmodules
7.3Applications
7.4Filtrations
7.5Gradingassociatedtoafiltration

8Inductivelimits
8.1Generalities
8.2Inductivesystemsofmaps
8.3Inductivesystemsofmagmas,groupsandrings
8.4Anexample
8.5Inductivesystemsofalgebras

9Sheavesoffunctions
9.1Sheaves
9.2Morphisms
9.3Sheafassociatedtoapresheaf
9.4Gluing
9.5Ringedspace

10Jordandecompositionandsomebasicresultsongroups
10.1Jordandecomposition
10.2Generalitiesongroups
10.3Commutators
10.4Solvablegroups
10.5Nilpotentgroups
……
11Algebraicsets
12Prevarietiesandvarieties
13Projectivevarieties
14Dimension
15Morphismsanddimension
16Tangent8paces
17Normalvarieties
18Rootsystems
19Liealgebras
20SemisimpleandreductiveLiealgebras
21Algebraicgroups
22Affinealgebraicgroups
23Liealgebraofanalgebraicgroup
24CorrespondencebetweengroupsandLiealgebras
25Homogeneousspace8andquotients
38SemisimplesymmetricLiealgebras
39SheetsofLiealgebras,
40Indexandlinearforms
References
Listofnotations
Index