图书信息
图书目录
对合之书（影印版）
暂无简介
作者：
Max-Albert Knus, Alexander Merkurjev, Markus Rost, Jean-Pier
定价：
269.00元
出版时间：
2020-04-22
ISBN：
978-7-04-053493-1
物料号：
53493-00
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：
998.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 前辅文
- Preface
- Introduction
- Conventions and Notations
- Chapter I. Involutions and Hermitian Forms
- § 1. Central Simple Algebras
- l.A. Fundamental theorems
- l.B. One-sided ideals in central simple algebras
- l.C. Severi-Brauer varieties
- §2. Involutions
- 2.A. Involutions of the first kind
- 2.B. Involutions of the second kind
- 2.C. Examples
- 2.D. Lie and Jordan structures
- §3. Existence of Involutions
- 3.A. Existence of involutions of the first kind
- 3.B. Existence of involutions of the second kind
- §4. Hermitian Forms
- 4.A. Adjoint involutions
- 4.B. Extension of involutions and transfer
- §5. Quadratic Forms
- 5.A. Standard identifications
- 5.B. Quadratic pairs
- Exercises
- Notes
- § 1. Central Simple Algebras
- Chapter II. Invariants of Involutions
- §6. The Index
- 6.A. Isotropic ideals
- 6.B. Hyperbolic involutions
- 6.C. Odd-degree extensions
- §7. The Discriminant
- 7. A. The discriminant of orthogonal involutions
- 7.B. The discriminant of quadratic pairs
- §8. The Clifford Algebra
- 8.A. The split case
- 8.B. Definition of the Clifford algebra
- 8.C. Lie algebra structures
- 8.D. The center of the Clifford algebra
- 8.E. The Clifford algebra of a hyperbolic quadratic pair
- §9. The Clifford Bimodule
- 9.A. The split case
- 9.B. Definition of the Clifford bimodule
- 9.C. The fundamental relations
- §10. The Discriminant Algebra
- 10.A. The A-powers of a central simple algebra
- 10.B. The canonical involution
- 10.C. The canonical quadratic pair
- 10.D. Induced involutions on A-powers
- 10.E. Definition of the discriminant algebra
- 10.F. The Brauer class of the discriminant algebra
- §11. Trace Form Invariants
- 11.A. Involutions of the first kind
- l l . B . Involutions of the second kind
- Exercises
- Notes
- §6. The Index
- Chapter III. Similitudes
- §12. General Properties
- 12.A. The split case
- 12.B. Similitudes of algebras with involution
- 12.C. Proper similitudes
- 12.D. Functorial properties
- §13. Quadratic Pairs
- 13.A. Relation with the Clifford structures
- 13.B. Clifford groups
- 13.C. Multipliers of similitudes
- § 14. Unitary Involutions
- 14.A. Odd degree
- 14.B. Even degree
- 14.C. Relation with the discriminant algebra
- Exercises
- Notes
- §12. General Properties
- Chapter IV. Algebras of Degree Four
- §15. Exceptional Isomorphisms
- 15.A. Bi = d
- 15.B. A\ = D2
- 15.C. B2 = C2
- 15.D. A3 = Ds
- §16. Biquaternion Algebras
- 16.A. Albert forms
- 16.B. Albert forms and symplectic involutions
- 16.C. Albert forms and orthogonal involutions
- §17. Whitehead Groups
- 17.A. SKi of biquaternion algebras
- 17.B. Algebras with involution
- Exercises
- Notes
- §15. Exceptional Isomorphisms
- Chapter V. Algebras of Degree Three
- §18. Etale and Galois Algebras
- 18.A. Etale algebras
- 18.B. Galois algebras
- 18.C. Cubic etale algebras
- §19. Central Simple Algebras of Degree Three
- 19.A. Cyclic algebras
- 19.B. Classification of involutions of the second kind
- 19.C. Etale subalgebras
- Exercises
- Notes
- §18. Etale and Galois Algebras
- Chapter VI. Algebraic Groups
- §20. Hopf Algebras and Group Schemes
- 20.A. Group schemes
- §21. The Lie Algebra and Smoothness
- 21.A. The Lie algebra of a group scheme
- §22. Factor Groups
- 22.A. Group scheme homomorphisms
- §23. Automorphism Groups of Algebras
- 23.A. Involutions
- 23.B. Quadratic pairs
- §24. Root Systems
- 24.A. Classification of irreducible root systems
- §25. Split Semisimple Groups
- 25.A. Simple split groups of type A, B, C, D, F , and G
- 25.B. Automorphisms of split semisimple groups
- §26. Semisimple Groups over an Arbitrary Field
- 26.A. Basic classification results
- 26.B. Algebraic groups of small dimension
- § 27. Tits Algebras of Semisimple Groups
- 27.A. Definition of the Tits algebras
- 27.B. Simply connected classical groups
- 27.C. Quasisplit groups
- Exercises
- Notes
- §20. Hopf Algebras and Group Schemes
- Chapter VII. Galois Cohomoiogy
- §28. Cohomoiogy of Profinite Groups
- 28.A. Cohomoiogy sets
- 28.B. Cohomoiogy sequences
- 28.C. Twisting
- 28.D. Torsors
- §29. Galois Cohomoiogy of Algebraic Groups
- 29.A. Hilbert's Theorem 90 and Shapiro's lemma
- 29.B. Classification of algebras
- 29.C. Algebras with a distinguished subalgebra
- 29.D. Algebras with involution
- 29.E. Quadratic spaces
- 29.F. Quadratic pairs
- §30. Galois Cohomology of Roots of Unity
- 30.A. Cyclic algebras
- 30.B. Twisted coefficients
- 30.C. Cohomological invariants of algebras of degree three . . . .
- §31. Cohomological Invariants
- 31.A. Connecting homomorphisms
- 3l.B. Cohomological invariants of algebraic groups
- Exercises
- Notes
- §28. Cohomoiogy of Profinite Groups
- Chapter VIII. Composition and Triality
- §32. Nonassociative Algebras
- §33. Composition Algebras
- 33.A. Multiplicative quadratic forms
- 33.B. Unital composition algebras
- 33.C. Hurwitz algebras
- 33.D. Composition algebras without identity
- §34. Symmetric Compositions
- 34.A. Para-Hurwitz algebras
- 34.B. Petersson algebras
- 34.C. Cubic separable alternative algebras
- 34.D. Alternative algebras with unitary involutions
- 34.E. Cohomological invariants of symmetric compositions . . . .
- §35. Clifford Algebras and Triality
- 35.A. The Clifford algebra
- 35.B. Similitudes and triality
- 35.C. The group Spin and triality
- §36. Twisted Compositions
- 36.A. Multipliers of similitudes of twisted compositions
- 36.B. Cyclic compositions
- 36.C. Twisted Hurwitz compositions
- 36.D. Twisted compositions of type A'2
- 36.E. The dimension 2 case
- Exercises
- Notes
- Chapter IX. Cubic Jordan Algebras
- §37. Jordan Algebras
- 37.A. Jordan algebras of quadratic forms
- 37.B. Jordan algebras of classical type
- 37.C. Freudenthal algebras
- §38. Cubic Jordan Algebras
- 38.A. The Springer decomposition
- §39. The Tits Construction
- 39.A. Symmetric compositions and Tits constructions
- 39.B. Automorphisms of Tits constructions
- §40. Cohomological Invariants
- 40.A. Invariants of twisted compositions
- §41. Exceptional Simple Lie Algebras
- Exercises
- Notes
- §37. Jordan Algebras
- Chapter X. Trialitarian Central Simple Algebras
- §42. Algebras of Degree 8
- 42.A. Trialitarian triples
- 42.B. Decomposable involutions
- §43. Trialitarian Algebras
- 43.A. A definition and some properties
- 43.B. Quaternionic trialitarian algebras
- 43.C. Trialitarian algebras of type 2D^
- §44. Classification of Algebras and Groups of Type D4
- 44.A. Groups of trialitarian type D4
- 44.B. The Clifford invariant
- §45. Lie Algebras and Triality
- 45.A. Local triality
- 45.B. Derivations of twisted compositions
- 45.C. Lie algebras and trialitarian algebras
- Exercise
- Notes
- §42. Algebras of Degree 8
- Bibliography
- Index
- Notation
