例外群及其几何(英文版)Exceptional groups and their geometry

本书介绍例外群的知识，分为三部分：理论、 应用及附录；共14章，包括经典群、复合代数、例 外若尔当代数、例外群的算术子群、例外李群上同 调、齐次空间、例外李群在理论物理和代数几何中 的应用等。 Bruce Hunt 于1986年在波恩大学取得博士学 位，导师是Frierich Hirzebruch（同时代数学家 中的领军人物）。Bruce Hunt 发表了“模簇、球 商、Calabi-Yau 簇”等方向的一系列论文，2021 年出版了获得五星好评的巨著《局部混合对称空间 》，也是《微分几何：曲线、曲面、流形（第三版 ）》一书的英文译者。

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