- 非结合代数在射影几何中的作用(英文版)(精)/美国数学会经典影印系列
- - 作者：(美)约翰·R.福克纳|责编:吴晓丽
  - 出版社：高等教育
  - ISBN：9787040632484
  - 出版日期：2025/02/01
  - 页数：229
- 售价：39.6

内容大纲
本书是我社正在开发的《美国数学会经典影印系列》中的一本，美国数学会的出版物在国际数学界享有很高声誉，出版了很多影响广泛的数学书。“十四五”期间计划引进的该学会的图书系列涵盖了代数、几何、分析、方程、拓扑、概率、动力系统等所有主要数学分支以及新近发展的数学主题。本书是非结合代数领域的经典著作，适合对非结合代数相关方向感兴趣的研究生和数学科研人员参考使用。本书是美国数学会出版的数学类经典学术著作。作者是世界知名数学专家，具有较高的学术水平，书稿整体质量较好。
作者介绍
目录
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(C(V))
  8.4.Simple groups
  8.5.Exercises
Chapter 9.Quadratic Forms and Orthogonal Groups
  9.1.Preview
  9.2.Quadratic formsidapin oldumonus buo shue
  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 HE,(C)
  11.3.Norms on H(Cn)
  11.4.Transitivity of HE,(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

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