Buildings of Spherical Type and Finite Bn-Pairs

By Jacques Tits

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.

• Format: Paperback
• Language: English
• ISBN: 3540067574
• ISBN13: 9783540067573
• Release Date: January 1974
• Publisher: Springer
• Length: 304 Pages
• Weight: 0.97 lbs.
• Dimensions: 0.7" x 6.1" x 9.2"