图书信息
图书目录
非结合代数在射影几何中的作用（影印版）
暂无简介
作者：
John R. Faulkner
定价：
99.00 元
出版时间：
2025-02-14
ISBN：
978-7-04-063248-4
物料号：
63248-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
代数学
重点项目：
暂无
版面字数：
390.00千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次印刷时间：
2025年
- 前辅文
- Introduction
- Chapter 1. Affine and Projective Planes
- §1.1. Preview
- §1.2. Incidence geometry
- §1.3. Affine planes
- §1.4. Projective planes
- §1.5. Duality
- §1.6. Exercises
- Chapter 2. Central Automorphisms of Projective Planes
- §2.1. Preview
- §2.2. Projections and automorphisms
- §2.3. Transvections and dilatations
- §2.4. Transitivity properties
- §2.5. Exercises
- Chapter 3. Coordinates for Projective Planes
- §3.1. Preview
- §3.2. Ternary systems
- §3.3. Two coordinatizations related to G(C)
- §3.4. Transvections and algebraic properties
- §3.5. Exercises
- Chapter 4. Alternative Rings
- §4.1. Preview
- §4.2. Left Moufang rings
- §4.3. Artin’s Theorem
- §4.4. Inverses in alternative rings
- §4.5. The Cayley-Dickson process
- §4.6. Composition algebras
- §4.7. Split and division composition algebras
- §4.8. Exercises
- Chapter 5. Configuration Conditions
- §5.1. Preview
- §5.2. Desargues condition
- §5.3. Quadrangle sections
- §5.4. Pappus condition
- §5.5. Configurations and central automorphisms
- §5.6. Exercises
- Chapter 6. Dimension Theory
- §6.1. Preview
- §6.2. Dimensionable sets
- §6.3. Independence and bases
- §6.4. Strongly dimensionable sets
- §6.5. Exercises
- Chapter 7. Projective Geometries
- §7.1. Preview
- §7.2. Projective and nearly projective geometries
- §7.3. Relation to strongly dimensionable sets
- §7.4. Classification of projective geometries
- §7.5. Exercises
- Chapter 8. Automorphisms of G(V)
- §8.1. Preview
- §8.2. The Fundamental Theorem
- §8.3. Subgroups of Aut(G(V ))
- §8.4. Simple groups
- §8.5. Exercises
- Chapter 9. Quadratic Forms and Orthogonal Groups
- §9.1. Preview
- §9.2. Quadratic forms
- §9.3. Orthogonal groups
- §9.4. Exercises
- Chapter 10. Homogeneous Maps
- §10.1. Preview
- §10.2. Polarization of homogeneous maps
- §10.3. Exercises
- Chapter 11. Norms and Hermitian Matrices
- §11.1. Preview
- §11.2. Hermitian matrices and HEn(C)
- §11.3. Norms on H(Cn)
- §11.4. Transitivity of HEn(C)
- §11.5. Trace and adjoint
- §11.6. H(C3)
- §11.7. Exercises
- Chapter 12. Octonion Planes
- §12.1. Preview
- §12.2. The construction of octonion planes
- §12.3. Simplicity of PHE3(O)
- §12.4. Automorphisms of octonion planes
- §12.5. Exercises
- Chapter 13. Projective Remoteness Planes
- §13.1. Preview
- §13.2. Definition and examples
- §13.3. Groups of Steinberg type
- §13.4. Transvections
- §13.5. Exercises
- Chapter 14. Other Geometries
- §14.1. Preview
- §14.2. Erlangen program
- §14.3. The geometry of R-spaces
- §14.4. Buildings
- §14.5. Generalized n-gons
- §14.6. Moufang sets and structurable algebras
- §14.7. Freudenthal-Tits magic square
- §14.8. Exercises
- Bibliography
- Index
