
Buildings of Spherical Type and Finite BN-Pairs
J. Tits(Author)
Springer (Publisher)
Published on 1. January 1974
Book
Paperback/Softback
XII, 304 pages
978-3-540-06757-3 (ISBN)
Description
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.
More details
Series
Edition
1st ed. 1974. Corr. 2nd printing 1986
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XII, 304 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 18 mm
Weight
482 gr
ISBN-13
978-3-540-06757-3 (9783540067573)
DOI
10.1007/978-3-540-38349-9
Schweitzer Classification
Content
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.