例外群及其幾何 (英文) 布魯斯.亨持 9787040636185 【台灣高等教育出版社】

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書名:例外群及其幾何 (英文)
ISBN:9787040636185
出版社:高等教育出版社
著編譯者:布魯斯.亨持
頁數:794
所在地:中國大陸 *此為代購商品
書號:1737666
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內容簡介 本書系統闡述例外群的理論體系及其應用,分為三大部分:理論篇、應用篇與附錄篇,共包含14個專題章節。核心內容涵蓋經典群結構、複合代數空間、例外若爾當代數、例外群的算術子群理論、例外李群上同調分析、齊次空間幾何等基礎理論,並深入探討了例外李群在理論物理前沿與代數幾何領域的重要應用。 作者Bruce Hunt師承20世紀數學巨擘F Hirze-bruch,1986年以優異成績獲得波恩大學博士學位。他在模簇分類、球商空間構造、Calabi-Yau簇形變理論等領域發表了一系列論文。其2021年出版的學術專著《局部混合對稱空間》獲得廣泛好評,同時是美國數學會出版的《微分幾何:曲線、曲面、流形(第三版)》的英文譯者。

目錄 Introduction
1 The classical groups
1 1 The classical compact simple Lie groups
1 1 1 Maximal Tori and the Weyl group
1 1 2 Principal bundles and classifying spaces
1 1 3 Lie algebras of classical type
1 2 Real Lie algebras and groups of classical type
1 2 1 Involutions
1 2 2 Real forms
1 3 Q-Lie algebras and arithmetic groups of classical type
1 3 1 Classification theorem
1 3 2 The Q-forms for groups of classical type
1 3 3 Picard modular groups
1 3 4 Siegel modular groups
1 4 Arithmetic quotients of Riemannian symmetric spaces
1 4 1 Commensurability
1 4 2 Picard modular varieties
1 4 3 Siegel modular varieties
Part Ⅰ Exceptional algebraic and Lie groups
2 Composition algebras and octonions
2 1 Alternative algebras
2 2 Composition algebras
2 3 The automorphism group of an octonion algebra
2 4 Derivations of an octonion algebra
2 5 Octonions and Clifford algebras
2 6 Triality
2 7 Lattices
2 8 The projective octonion line and Bott periodicity
3 Exceptional Jordan algebras and F
3 1 Jordan algebras
3 2 Classification
3 3 Jordan triple syems
3 4 Albert algebras
3 5 Orders in Jordan algebras
4 The exceptional complex Lie groups and their real forms
4 1 The Tits-Vinberg-Atsuyama conructions
4 2 Adams』 conruction
4 3 Freudenthal』s conruction
5 Q-forms and arithmetic subgroups of exceptional groups
5 1 Twied composition algebras and exceptional D
5 2 Descriptions of the Q-forms for E6, E
6 Cohomology of exceptional Lie groups and homogeneous spaces
6 1 Generators of cohomology
6 2 Exceptional Hermitian symmetric spaces
6 3 Some geometry of exceptional homogeneous spaces
6 4 Cohomology of the exceptional groups
7 Exceptional groups and projective planes
7 1 Real projective spaces
7 2 Projective planes
Part Ⅱ Applications of exceptional groups
8 Applications of octonions and exceptional Lie groups in theoretical physics
8 1 Division algebras and the andard model in theoretical physics
8 2 Division algebras and particles
8 3 Jordan algebras and the andard model
8 4 Exceptional homogeneous spaces arising from compactifications of supergravity
8 5 Some other occurrences of exceptional groups
9 Applications of exceptional groups in algebraic geometry
9 1 Unimodular surface singularities and orbits of Lie groups in the adjoint representation
9 2 Arrangements
9 3 The Weyl group W(F4) and related geometry
9 4 The Weyl group W(A5) and related geometry
9 5 The Weyl group W(E6) and related geometry
9 6 The Weyl group W(E7) and related geometry
9 7 The Weyl group W(E8) and related geometry
9 8 Solving algebraic equations and the resolvent degree
9 9 Del Pezzo surfaces
9 10 K3 surfaces
Part Ⅲ Appendices
10 Root syems
Fiber bundles and homogeneous spaces
1 Topological results
2 Lie groups and representations
12 Clifford algebras
12 1 Algebraic formulation
12 2 Minkowski space
12 3 Bott periodicity
12 4 Spin, semispin and orthogonal groups
12 5 Spin representations
12 6 Gamma matrices
13 Some algebraic geometry
13 1 Plane curves
13 2 Singularities and resolutions
13 3 Algebraic groups
13 4 Moduli spaces
13 5 Ball quotients
14 Classical and quantum mechanics and field theory
14 1 Group representations and physics
14 2 Lagrangian and Hamiltonian mechanics
14 3 Electromagnetics
14 4 Gravity
14 5 Quantization
14 6 Gauge theories
14 7 Quantum field theory
14 8 Supersymmetry and supergravity
14 9 Superrings and compactifications
14 10 Dualities
References
Index

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