02909nam 2200457 450 99646653590331620230213211550.03-540-38349-210.1007/978-3-540-38349-9(DE-He213)978-3-540-38349-9(MiAaPQ)EBC3088979(MiAaPQ)EBC6575211(Au-PeEL)EBL6575211(OCoLC)1255224075(EXLCZ)99100000000043841420211210h19861974 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierBuildings of spherical type and finite BN-pairs /J. Tits1st ed. 1974.Berlin, Germany :Springer,[1986]©19741 online resource (XII, 304 p.) Lecture Notes in Mathematics,0075-8434 ;386Complexes -- 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.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.Lecture Notes in Mathematics,0075-8434 ;386Buildings (Group theory)Buildings (Group theory)512.2Tits Jacques42019MiAaPQMiAaPQMiAaPQBOOK996466535903316Buildings of spherical type and finite BN-pairs81519UNISA