Buildings of spherical type and finite BN-pairs / / J. Tits

• Autore: Tits Jacques
• Pubblicazione: Berlin, Germany : , : Springer, , [1986]; ©1974
• Edizione: 1st ed. 1974.
• Descrizione fisica: 1 online resource (XII, 304 p.)
• Disciplina: 512.2
• Soggetto topico: Buildings (Group theory)
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Buildings of spherical type and finite BN-pairs
• ISBN: 3-540-38349-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466535903316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 386