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Buildings of Spherical Type and Finite BN-Pairs

  • Book
  • © 1974

Overview

Authors:
  1. Jacques Tits

    1. Collège de France, Paris Cedex 05, France

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 386)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-X
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  2. Complexes

    Pages 1-12

  3. Coxeter complexes

    Pages 13-37

  4. Buildings

    Pages 38-59

  5. Reduction

    Pages 60-74

  6. The building of a semi-simple algebraic group

    Pages 75-91

  7. Buildings of type An, Dn, En

    Pages 92-101

  8. Buildings of type Cn. I. Polar spaces

    Pages 102-116

  9. Buildings of type Cn. II. Projective embeddings of polar spaces

    Pages 117-176

  10. Buildings of type Cn. III. Non-embeddable polar spaces

    Pages 177-199

  11. Buildings of type F4

    Pages 200-217

  12. Finite BN-pairs of irreducible type and rank ≥ 3

    Pages 218-231

  13. Appendix 1. Shadows

    Pages 232-248

  14. Appendix 2. Generators and relations

    Pages 249-273

  15. Back Matter

    Pages 274-302
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Keywords

About this book

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.

Authors and Affiliations

  • Collège de France, Paris Cedex 05, France

    Jacques Tits

Bibliographic Information

  • Book Title: Buildings of Spherical Type and Finite BN-Pairs

  • Authors: Jacques Tits

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-38349-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1974

  • Softcover ISBN: 978-3-540-06757-3Published: 01 January 1974

  • eBook ISBN: 978-3-540-38349-9Published: 05 February 2009

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 304

  • Topics: Algebra

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