Buildings of Spherical Type and Finite BN-Pairs

  • Jacques Tits
Part of the Lecture Notes in Mathematics book series (LNM, volume 386)

About this book

Introduction

These notes are a slightly revised and extended version of mim- graphed notes written on the occasion of a seminar on buildings and BN-pairs held at Oberwolfach in April 1968. Their main purpose is to present the solution of the following two problems: (A) Determination of the buildings of rank >; and irreducible, spherical type, other than ~ and H ("of spherical type" means "with finite Weyl 4 group", about the excluded types H, cf. the addenda on p. 274). Roughly speaking, those buildings all turn out to be associated to simple algebraic or classical groups (cf. 6. ;, 6. 1;, 8. 4. ;, 8. 22, 9. 1, 10. 2). An easy application provides the enumeration of all finite groups with BN-pairs of irreducible type and rank >;, up to normal subgroups contained in B (cf. 11. 7). (B) Determination of all isomorphisms between buildings of rank > 2 and spherical type associated to algebraic or classical simple groups and, in parti­ cular, description of the full automorphism groups of such buildings (cf. 5. 8, 5. 9, 5. 10, 6. 6, 6. 1;, 8. 6, 9. ;, 10. 4). Except for the appendices, the notes are rather strictly oriented - ward these goals.

Keywords

Finite Morphism algebra algebraic group automorphism finite group

Authors and affiliations

  • Jacques Tits
    • 1
  1. 1.Collège de FranceParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-38349-9
  • Copyright Information Springer Berlin Heidelberg 1974
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-06757-3
  • Online ISBN 978-3-540-38349-9
  • Series Print ISSN 0075-8434