Jacques Tits, Œuvres – Collected Works
Volume IV
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 They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now.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. 1–43 [128] Schémas en groupes et immeubles des groupes classiques sur un corps localpp. 44–52 [129] On R. Griess’ “Friendly giant”pp. 53–70 [130] Le Monstre (d’après R. Griess, B. Fischer et al.)pp. 71–101 [132] Groups and group functors attached to Kac-Moody datapp. 102–116 [133] On generalized hexagons and a near octagon whose lines have three pointspp. 117–148 [135] Immeubles de type affinepp. 149–169 [136] Ensembles ordonnés, immeubles et sommes amalgaméespp. 170–176 [137] La vie et l’oeuvre de Claude Chevalleypp. 177–181 [138] On discrete chamber-transitive automorphism groups of affine buildingspp. 182–213 [139] Uniqueness and presentation of Kac–Moody groups over fieldspp. 214–231 [140] Buildings and group amalgamationspp. 232–286 [141] Schémas en groupes et immeubles des groupes classiques sur un corps local, II. Groupes unitairespp. 287–314 [142] Groupes algébriques sur un corps local, III. Compléments et applications à la cohomologie galoisiennepp. 315–333 [143] Le module du “Moonshine" (d’après I. Frenkel, J. Lepowsky et A. Meurman)pp. 334–339 [144] Sur le groupe des automorphismes de certains produits en couronnepp. 340–355 [145] Building buildingspp. 356–366 [146] Geometrie von Raum, Zeit und Kausalität: Ein axiomatischer Zugangpp. 367–386 [147] Unipotent elements and parabolic subgroups of reductive groups, IIpp. 387–391 [148] Groupes de type E sur les corps globauxpp. 392–403 [149] Sur le groupe des automorphismes de certains groupes de Coxeterpp. 404–428 [150] Groupes associés aux algèbres de Kac–Moodypp. 429–458 [151] Strongly inner anisotropic forms of simple algebraic groupspp. 459–470 [152] Spheres of radius 2 in triangle buildings, Ipp. 471–482 [153] Symmetrie 1pp. 483–489 [154] The inverse of a Cartan matrixpp. 490–506 [155] Twin trees, Ipp. 507–509 [156] Sur les produits tensoriels de deux algèbres de quaternionspp. 510–523 [157] Moufang polygons, I. Root datapp. 524–561 [158] Twin buildings and groups of Kac–Moody typepp. 562–569 [159] Sur les degrés des extensions de corps déployant les groupes algébriques simplesp. 570 [160] Ein Fixpunktsatz für Gebäude und Anwendungenpp. 571–599 [161] Twin trees, II. Local structure and a universal constructionpp. 600–627 [162] Discreteness criteria for tree automorphism groupspp. 628–647 [164] The center conjecture for non-exceptional buildingspp. 648–652 [A4] Armand Borel as I knew himpp. 653–565 [A5] Quarante-cinq et cent numéros des Publications Mathématiques de l’I.H.É.S. Quelques souvenirspp. 657–740 [B1] Lectures on algebraic groupspp. 741–828 [B2] Affine buildings, arithmetic groups and finite geometriespp. 829–951 [C1] Les espaces doublement homogènes et les espaces homogènes et isotropespp. 952–968 [C2] The Cremona planepp. 969–1000 [C5] Some remarks on Griess’ construction of the Griess–Fischer sporadic group (I), (II), (III), (IV)pp. 1001–1006 Notes of the Editorspp. 1007–1008 Acknowledgementspp. 1009–1020 Liste complète des publications / Complete list of publications