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001 978-3-540-38349-9
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008 121227s1974 gw | s |||| 0|eng d
020 _a9783540383499
_9978-3-540-38349-9
024 7 _a10.1007/978-3-540-38349-9
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aTits, Jacques.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBuildings of Spherical Type and Finite BN-Pairs
_h[electronic resource] /
_cby Jacques Tits.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1974.
300 _aXII, 304 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v386
505 0 _aComplexes -- 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.
520 _aThese 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.
650 0 _aAlgebra.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662165782
776 0 8 _iPrinted edition:
_z9783540067573
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v386
856 4 0 _uhttps://doi.org/10.1007/978-3-540-38349-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9805
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