Abramenko P. — Twin Buildings and Applications to S-Arithmetic Groups, Vol. 164 :: Электронная библиотека попечительского совета мехмата МГУ

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Abramenko P. — Twin Buildings and Applications to S-Arithmetic Groups, Vol. 164

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Название: Twin Buildings and Applications to S-Arithmetic Groups, Vol. 164

Автор: Abramenko P.

Аннотация:

This book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces - presupposing good knowledge of ordinary buildings - the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 123

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\Gamma$ -CW-complex      46
$\Gamma$ -restriction      41 42
Affine Weyl group      16
Almost simple k-group      9 19 107f.
Anisotropic algebraic group      3
Anisotropic subspace      78
Arithmetic group      1 2
Birkhoff decomposition      13 23
BN-pair      see Tits system
Bruhat decomposition      11 13 14
Bruhat-Tits building      4 5 19 112
Building of type M      21
Chevalley group      3 5 18f. 33 53
Classical group      1 107 112
Classical spherical building      8 68
Coconvex hull      40
Coconvex pair of subcomplexes      39
Codistance      22f.
Compact hyperbolic type      10 45
Coprojection      34 36f.
Cotype of a simplex      21
Coxeter complex      14
Coxeter matrix      12
Coxeter system of type M      12
d-spherical      7 45f.
Echelonnage      112
Eilenberg — MacLane complex      2 4
Finiteness length      4 45 112
Flag complex      68 72
Form parameter      77
Generalized m-gon      7 59f.
Global field      2 3 4
Group of type,       2 9 46 51f. 113f.
Group of type,       2 9 46 51f. 113f.
Hermitian form      78
Hyperbolic space over K      91
Isometry group      107f.
Isotropic algebraic group      3 107
Isotropic subspace      78
Join of simplicial complexes      42
Join of spherical buildings      57
Kac — Moody group      5 10 20 53f.
Laurent polynomial ring      17
Moufang building      8 50 69
Moufang generalized m-gon      59f.
n-generating      67

Negative root      14
Non-degenerate subspace      78
Opposite chambers      22f.
Opposite foldings      14
Opposite parabolic subgroups      5 11 20
Opposite roots      14
Opposition involution      38 56
Opposition isomorphism for twin apartments      27
Panel      7 27
Positive root      14
Prenilpotent pair of roots      14
Projection in a building      33 38
Pseudo-quadratic form      78
Quartier      5 33
Reductive group      2 3 4 11
Relative link      6 7 42 71
RGD-system      12 15f. 49 111
Root datum      11 58 110
Root group $U_{\alpha}$       11 15 17f. 59f. 111
Root of a Coxeter complex      14
Root system      11 16 110
S-arithmetic group      2 3 4 113
Saturated twin BN-pair      29
Semisimple algebraic group      1 2 114
Simplicial fundamental domain =: sfd      31 32 33 41
Spherical building      7 8 23 43 44 56f.
Spherical complex      see d-spherical
Spherical cotype      21
Spherical simplex      21
Strongly transitive action      28
Tits system (of type M)      11 12f.
Totally degenerate subspace      78
Totally isotropic subspace      78
Trace valued hermitian form      78
Transversal subspaces      74
Twin apartment      24f.
Twin BN-pair (of type M)      5 12f.
Twin building (of type M)      5 22f.
Twin root      40
Twin tree      51 52
Type of a gallery      21
Type of a simplex      21
W-codistance      see codistance
W-distance in buildings      22
Weyl group      11 12f. 110
Witt index      78

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