Buildings of Spherical Type and Finite Bn-Pairs

ISBN-13: 9783540067573 / Angielski / Miękka / 1974 / 304 str.

J. Tits

Opis

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.

Spis treści

Complexes.- Coxeter complexes.- Buildings.- Reduction.- The building of a semi-simple algebraic group.- Buildings of type An, Dn, En.- Buildings of type Cn. I. Polar spaces.- Buildings of type Cn. II. Projective embeddings of polar spaces.- Buildings of type Cn. III. Non-embeddable polar spaces.- Buildings of type F4.- Finite BN-pairs of irreducible type and rank ? 3.- Appendix 1. Shadows.- Appendix 2. Generators and relations.