有限域上典型群的几何学（第2版）（英文版）

图书标准信息

• 作者 万哲先 著
• 出版社 科学出版社
• 出版时间 2006-03
• 版次 2
• ISBN 9787030105950
• 定价 76.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 460页
• 正文语种 英语

【内容简介】

Thismonographisacomprehensivesurveyoftheresultsobtainedonthegeometryofclassicalgroupsoverfinitefieldsmainlyinthe1960sandearly1990s.FortheconvenienceofthereadersIstartwiththeaffinegeometryandprojectivegeometryoverfinitefieldsinChapters1and2，respectively.Amongotherthings，theaffineclassificationofquadricsisincludedinChapter1，andconicsandovalsarestudiedindetailinChapter2.FromChapter3andonwardsthegeometriesofsymplectic，pseudo-symplectic，unitary，andorthogonalgroupsarestudiedinsuccession.Thebookendswithtwoappendices，ontheaxiomaticprojectivegeometry，andonpolarspacesandfinitegeneralizedquadrangles，respectively.

【目录】

PrefacetotheSecondEdition
Preface
Chapter1AffineGeometryoverFiniteFields
1.1VectorSpacesandMatricesoverFiniteFields
1.2AffineSpacesandAffineGroupsoverFiniteFields
1.3QuadricsinAG（n，Fq）forqOdd
1.4QuadricsinAG（n，Fq）forqEven
1.5Comments
1.6Exercises
Chapter2ProjectiveGeometryoverFiniteFields
2.1ProjectiveSpacesandProjectiveGroupsoverFiniteFields
2.2QuadricsinPG（n，Fq）
2.3ConicsinPG（n，Fq）
2.4OvalsinPG（n，Fq）
2.5Comments
2.6Exercises
Chapter3GeometryofSymplecticGroupsoverFiniteFields
3.1SymplecticGroupsandSymplecticSpacesoverFiniteFields
3.2AnzahlTheoremsinSymplecticGeometryoverFiniteFields
3.3SingularSymplecticGeometryoverFiniteFields
3.4SymplecticPolaritiesandPolarSpacesArisingfromThem
3.5Comments
3.6Exercises
Chapter4GeometryofPseudo-symplecticGroupsoverFiniteFieldsofCharacteristic2
4.1Pseudo-symplecticGroupsoverFiniteFieldsofCharacteristic2
4.2Pseudo-symplecticGeometryoverFiniteFieldsofCharacteristic2
4.3SingularPseudo-symplecticGeometryoverFiniteFieldsof
Characteristic2
4.4Pseudo-symplecticGeometryoverFiniteFieldsofCharacteristic2Again
4.5Pseudo-symplecticPolarities
4.6Comments
4.7Exercises
Chapter5GeometryofUnitaryGroupsoverFiniteFields
5.1UnitaryGeometryoverFiniteFields
5.2AnzahlTheoremsinUnitaryGeometryoverFiniteFields
5.3SingularUnitaryGeometryoverFiniteFields
5.4UnitaryPolaritiesandPolarSpacesArisingfromThem
5.5HermitianvarietiesinPG（n，Fq2）andAG（n，Fq2）
5.6Comments
5.7Exercises
Chapter6GeometryofOrthogonalGroupsoverFiniteFie.idsofOddCharacteristic
6.1OrthogonalGeometryoverFiniteFieldsofOddCharacteristic
6.2AnzahlTheoremsinOrthogonalGeometryoverFiniteFieldsofOddCharacteristic
6.3SingularOrthogonalGeometryoverFiniteFieldsofOddCharacteristic
6.4OrthogonalPolaritiesandPolarSpacesArisingfromThem
6.5Comments
6.6Exercises
Chapter7GeometryofOrthogonalGroupsoverFiniteFieldsofCharacteristic2
7.1OrthogonalGeometryoverFiniteFieldsofCharacteristic2
7.2AnzahlTheoremsinOrthogonalGeometryoverFiniteFieldsofCharacteristic2
7.3SingularOrthogonalGeometryoverFiniteFieldsof
Characteristic2
7.4PolarSpacesArisingfromOrthogonalGeometryoverFiniteFieldsofCharacteristic2
7.5Comments
7.6Exercises
AppendixAAxiomaticProjectiveGeometry
A.1IncidenceStructures
A.2AxiomsofProjectivePlanesandthePrincipleofDuality.
A.3FiniteProjectivePlanes
A.4CollineationsinProjectivePlanes
A.5DesarguesPlanes
A.6ProjectiveSpaces
AppendixBPolarSpacesandGeneralizedQuadrangles..
B.1PolarSpaces
B.2GeneralizedQuadrangles
AppendixCCriticalProblems
C.1ACriticalProbleminFiniteVectorSpaces
C.2CriticalProblemsinFiniteUnitarySpaces
C.3ACriticalProbleminFiniteSymplecticSpaces
C.4Comments
AppendixDMoor-PenroseGeneralizedInversesofMatricesoverFiniteFields
D.1DefinitionandProperties
D.2ConstructionofEnumerationofM-PInvertibleMatrices.
D.3GeneralizationtoMatricesoverFq2
D.4Comments
AppendixERepresentationsofFormsbyFormsinaFiniteField
E.1RepresentationsofBilinearForms
E.2RepresentationsofAlternateForms
E.3RepresentationsofHermitianForms
E.4RepresentationsofQuadraticForms（OddCharacteristicCase）
E.5RepresentationsofQuadraticForms（EvenCharacteristicCase）
E.6RepresentationsofSymmetricBilinearFormsoverFiniteFieldsofEvenCharacteristic
E.7Comments
E.8Exercises
Bibliography
Notation
Index