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Brown K.S. — Buildings
Brown K.S. — Buildings



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Название: Buildings

Автор: Brown K.S.

Аннотация:

This book gives an introduction to Jacques Tit's theory of buildings, a subject in which there is a rich interplay between group theory and geometry. The book starts from scratch, with a discussion of finite reflection groups, and takes the reader to the literature on buildings. The prerequisites are kept to a minimum, and careful attention is paid to motivating new concepts that are introduced. The book should be accessible to any mathematics graduate student who knows very little group theory and topology.


Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 224

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathbf{R}$-tree      206
Absolutely almost simple      203
Action condition      35
Adjacent      13 29 31 34 59
Affine algebra      200
Affine building      151
Affine concepts      139—140
Affine reflection group      141
Affine Weyl group      148
Algebraic group      201
Almost simple      203
Alperin-Shalen theorem      194
Alperin—Shalen theorem      194
Alternating form      120
Apartment      76
Arithmetic group      183—184
Barycentric subdivision      28
BN-pair      110
Borel subgroup      203
Borel — Serre compactification      186 190
Bornological group      161
Bornology      161
Bounded set      160—161
Bounded subgroups      159ff
Bruhat decomposition      104 115
Building      76
Building at infinity      174ff
Canonical labelling      59
Canonical map      90
Canonical representation      55
CD      185
cell      6ff 141
Chamber      9 29 34 141
Chamber complex      29
Chamber map      30
Chamber system      31 63
Circumcenter      158
Circumradius      157
Closed cell      8
Coboundary      159
Cocompact      185
Cocycle      159
Cohen-Macaulay complex      94
Cohomological dimension      185
Combinatorial distance      14 34
Commensurable      184
Compact subgroups      159ff
Complete system of apartments      88
Completion      130
Conical cell      164 169
Connected group      203
Convex hull      93
Convex subcomplex      15 68 88
Convex subset      166
Cosine inequality      169
Coxeter complex      33 58 71
Coxeter condition      52
Coxeter diagram      22 60 78
Coxeter group      33 52—53
Coxeter matrix      21 54 78
Coxeter system      53
Cry st allograph ic      146
Deletion condition      37 73—74
Diameter      15 61
Dihedral group      3 37
DIMENSION      27
Direction      164
Discrete valuation      127
Discrete valuation ring      127
Distance      14 15 34 89 151
Dual of a regular solid      4
Elementary divisors      129
Elementary M-operation      49
END      176
Essential      2 11 143
Euclidean BN-pair      160
Euclidean building      151
Euclidean Coxeter complex      149
Euclidean reflection group      144
Euclidean space      150
Exchange condition      46
Extension of scalars      200
Face      7 27 33 177
Face at infinity      175
Feit — Higman theorem      117
Finite reflection group      1
Finiteness conditions      193
Finiteness length      193
Fixed-point theorem      157
fl      185
Flag      28
Flag complex      28
Folding      48 66
Folding condition      47
Frame      84 139
Fundamental apartment      99
Fundamental chamber      34 99
gallery      13 29 34
Generalized BN-pair      126 134—135
Generalized m-gon      117
Geodesic      94 155
Geometric realization      28
girth      87
Good apartment system      179
Group scheme      198
Half-space      35 70
Hirsch rank      189
Hopf algebra      200
Hyperplane      1
Ideal point      175
Ideal simplex      175
Idempotent      66
Incidence geometry      79
Irreducible      4 23 56
Irreducible components      23
Isotropic subspace      122
Join      63
Joinable simplices      29
Jordan-Holder permutation      84 105
Labelling      29
Lattice      128 145
Length      13 34
Linear algebraic group      201
Linear part      140
Link      31
M-reduced      49
midpoint      156
Midpoint convex      156
Minimal gallery      14
Monomial group      101
Monomial matrix      4
Negative curvature      155ff
Open cell      8
Opposite chamber      92
Opposite folding      69
Opposite half-space      70
Opposite parabolics      115
Oriflamme geometry      126
Orthogonal group      124
p-adic integers      130
p-adic numbers      130
p-adic valuation      128
Parabolic subgroup      112
parallel      172 174
Polar geometry      82—83 122
POSET      12 27
Projective geometry      81ff
Projective plane      81
Proper action      185
Property (NC)      156
Quartier      164
Rank      27 30 204
Ray      174
Reduced decomposition      46
Reduced word      46
Reductive group      203
Reflection      1 33 39 71 140
Regular solid      2
Residue field      128
Retraction      30 66 85ff 170—171
Reversible folding      69
Root system      2
s-adjacent      34
S-arithmetic group      189 196
Saturated BN-pair      114
Sector      164 169
Semisimple group      203
Simplicial complex      24 27
Simplicial cone      11
Simplicial map      30
Simply connected group      204
Solomon-Tits theorem      93ff
Special coset      26 33 111
Special orthogonal group      124
Special subgroup      26 110
Spherical building      92
Spherical Coxeter complex      92
Standard uniqueness argument      69 71
Star      154—155
Stretched      89
Strong isometry      90
Strongly transitive      99
Stuttering gallery      13
Subcomplex      15 27
Subsector      164
Support      7 141
Symmetric space      184 189
Symplectic group      121
System of apartments      76
Thick chamber complex      77
Thin chamber complex      58
Tits system      110
Torus      202
Totally isotropic subspace      122
Type $F_n$      193
Type FL      185
Type of a gallery      73—74
Type of a simplex      30
Type VFL      188
Type-preserving      58
Unipotent      202
Valuation      127
Valuation ring      127
vcd      188
VFL      188
Virtual cohomological dimension      188
wall      10 34 70 141
Walls crossed      14 34
Weak BN-pair      127
Weak building      77
Weyl group      2 110 115
Word      46
Word problem      49
Zariski topology      203
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