Jacques Tits, Œuvres – Collected Works
Volume III
Editors
Francis Buekenhout
Université libre de Bruxelles, BelgiumBernhard Mühlherr
Justus Liebig University Giessen, GermanyJean-Pierre Tignol
Université catholique de Louvain, BelgiumHendrik van Maldeghem
Ghent University, Belgium
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Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Tits’ papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac–Moody groups and on what subsequently became known as the Tits-alternative.
These volumes contain an almost complete collection of Tits’ mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Tits’ contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and BN-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Tits’ mathematical writings, these volumes contain biographical data, survey articles on aspects of Tits’ work and comments by the editors on the content of some of his papers.
With the publication of these volumes, a major piece of 20th century mathematics is being made available to a wider audience.
pp. i–iv Frontmatterpp. v–xi Contentspp. 1–246 [88] Groupes réductifs sur un corps local, I. Données radicielles valuées (avec F. Bruhat)pp. 247–270 [89] Compléments à l’article: “Groupes réductifs” (avec A. Borel)pp. 271–282 [90] Non-existence de certaines extensions transitives. I. Groupes projectifs à une dimensionpp. 283–292 [91] Une propriété des systèmes de racines (appendice à l’article de J. Dixmier: “Sur les homomorphismes d’Harish-Chandra”)pp. 293–365 [92] Homomorphismes “abstraits” de groupes algébriques simples (avec A. Borel)pp. 366–386 [93] Homomorphismes “abstraits” de groupes de Liepp. 387–389 [94] Une propriété des produits directs infinis de groupes finis isomorphes (avec S. Koppelberg)pp. 390–401 [95] On buildings and their applicationspp. 402–407 [96] Leçon inaugurale de la Chaire de Théorie des groupespp. 408–424 [97] Travaux de Margulis sur les sous-groupes discrets de groupes de Liepp. 425–428 [98] Two properties of Coxeter complexes (Appendix to “A Mackey formula in the group ring of a Coxeter group” by L. Solomon)pp. 429–438 [99] Non-existence de certains polygones généralisés,Ipp. 439–441 [100] Systèmes générateurs de groupes de congruencepp. 442–459 [101] Classification of buildings of spherical type and Moufang polygons: a surveypp. 460–471 [102] A “theorem of Lie–Kolchin” for treespp. 472–487 [103] Quadrangles de Moufang, Ipp. 488–498 [104] Projective representations of minimum degree of group extensions (with W. Feit)pp. 499–511 [105] Endliche Spiegelungsgruppen, die als Weylgruppen auftretenpp. 512–519 [106] Sur certains groupes dont l’ordre est divisible par 23pp. 520–538 [107] Groupes de Whitehead de groupes algébriques simples sur un corps (d’après V. P. Platonov et al.)pp. 539–541 [108] Théorèmes de structure et de conjugaison pour les groupes algébriques linéaires (avec A. Borel)pp. 542–582 [109] Reductive groups over local fieldspp. 583–589 [110] The work of Gregori Aleksandrovitch Margulispp. 590–592 [111] Non-existence de certaines polygones généralisés, II (avec F. Bruhat)pp. 593–602 [112] Spherical buildings and the character of the Steinberg representation (with C. W. Curtis and G. I. Lehrer)pp. 603–622 [113] Quaternions over Q[], Leech’s lattice and the sporadic group of Hall–Jankopp. 623–649 [114] Le principe d’inertie en relativité généralepp. 650–654 [115] Four presentations of Leech’s latticepp. 655–666 [116] Buildings and Buekenhout geometriespp. 667–671 [119] Appendix to the article “Groups of polynomial growth and expanding maps” by M. Gromovpp. 672–677 [120] Définition par générateurs et relations de groupes avec BN-pairespp. 678–690 [122] Groupes à croissance polynomiale (d’après M. Gromov et al.)pp. 691–719 [123] A local approach to buildingspp. 720–729 [124] Evariste Galois, son oeuvre, sa vie, ses rapports avec l’Académiepp. 730–785 [125] Moufang octagons and the Ree groups of typepp. 786–788 [126] On the distance between opposite vertices in buildings of spherical type (appendix to the article “Some remarks on Tits geometries” by A. E. Brouwer and A. M. Cohen)pp. 789–968 [127] Groupes réductifs sur un corps local, II. Schémas en groupes. Existence d’une donnée radicielle valuée (avec F. Bruhat)pp. 969–971 Notes of the Editorspp. 973–974 Acknowledgementspp. 975–986 Liste complète des publications / Complete list of publications