非结合代数在射影几何中的作用（影印版）

样章

作者：

John R. Faulkner

定价：

99.00 元

版面字数：

390千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-063248-4

物料号：

63248-00

出版时间：

2025-02-14

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

暂无

目录
- 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