Buildings of Spherical Type and Finite BN-Pairs

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Januar 1986



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.


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.
EAN: 9783540067573
ISBN: 3540067574
Untertitel: 1st ed. 1974. Corr. 2nd printing 1986. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Januar 1986
Seitenanzahl: 316 Seiten
Format: kartoniert
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