Parshin A.N., Shafarevich I.R. — Algebraic Geometry IV: Linear Algebraic Groups Invariant Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Parshin A.N., Shafarevich I.R. — Algebraic Geometry IV: Linear Algebraic Groups Invariant Theory

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Название: Algebraic Geometry IV: Linear Algebraic Groups Invariant Theory

Авторы: Parshin A.N., Shafarevich I.R.

Аннотация:

This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a well-known expert in the first mentioned field. He presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of part two, E.B. Vinberg and V.L. Popov, are among the most active researchers in invariant theory. The last 20 years have been a period of vigorous development in this field due to the influence of modern methods from algebraic geometry. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

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Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 284

Добавлена в каталог: 12.03.2005

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Предметный указатель

Abels, H.      115
Action, good rational      147
Action, locally transitive      217
Action, rational      146
Action, regular      146
Action, stable      156
Action, triangular      162 Algebra algebraic
Adamovich, O.M.      247 258 260
Adams, J.F.      179
Affine group scheme      12
Akhiezer, D.N.      264
Aleksandrov, P.S.      171
Alekseev, V.G.      264
Alekseevskij, A.V.      246
Algebra, algebraic Lie      86
Algebra, Cohen — Macaulay      178
Algebra, Lie      16
Algebra, Lie of covariants      184
Algebra, Lie of distributions      18
Algebra, Lie of invariants      131 164
Andreev, E.M.      234
Antonyan, L.V.      246 261 262
Apartment      101
Apolar      141
Armstrong, M.A.      242
Arnol’d, V.I.      145 218 227
A’Campo, A.      171
Bardsley, P.      265
Basis of a root system      31
Beklemishev, N.D.      216 238
Bialynicki-Birula, A.      172 215 221
Birkes, D.      199 215
Bogomolov, F.A.      163 164 194 201
Borel, A.      4 6 23 28 29 39 48—50 54 55 57—59 61 62 64 65 67 68 71 73 84 87 90 91 112 114—116 118
Borel’s fixed point theorem      24
Borho, W.      197 198 219 220 221
Bourbaki, N.      30 31 34 36 40 47 71 72 79 87 88 92 97 98 103 107 239 240 255
Boutot, J-F.      176
Bredon, G.E.      207 214 216 228
Brion, M.      227 232
Brouwer, A.E.      180
Browder, F.E.      171
Bruhat, F.      51 101 102 104 105 107 108
Bruhat’s lemma      33
Bui Viet Kha      216
Building, affine      104
Building, spherical Tits      74
Carrell, J.B.      250
Cartan decomposition      93 107
Carter, R.W.      59 97 99 100
Cernousov, V.I.      118
Chanler, J.H.      276
CHARACTER      21
Characteristic of a nilpotent element      201
Chevalley, C.      5 6 39 87 152 187 214 240
Class number      115
Cocharacter      21
Cohen, A.M.      180
Cone, asymptotic      197
Congruence Subgroup Problem      112
Covariant      181
Criterion, Hilbert — Mumford      198
Criterion, Igusa’s      190
Criterion, Kempf — Ness      223
Criterion, Luna’s      222
Criterion, Matsushima’s      194
Cross-ratio      138
Curtis, C.W.      74 75 100
Dadok, J.      224 246 248
de Concini, C.      266
Demazure, M.      6 12 16 18 39 51 54 59 63 64
Dickson, L.E.      266
Dieudonne, J.A.      250
Differential equations for invariants      167
Direct product      13
Discriminant of a binary form      141
Dixmier, J.      142 219 238 266
Djokovic, D.Z.      246
Doan Quynh      266
Dolgachev, I.V.      163
Donaldson, S.      227
Donkin, S.      267
Dynkin diagram      40
Dynkin diagram, affine      103
Dynkin, E.B.      201 204 233 245
Egorov, G.V      258 261
Ehlashvili, A.G.      221 234 246 261 262
Element, nilpotent      197
Element, rational semisimple      201
Element, reduced      202
Element, semisimple      214
Elliot, E.B.      267
Erdos, P.      266
F-rank      68
F-rank, semi-simple      68
Fiber space, homogeneous      194
Fiber space, locally isotrivial      195
Fibering, locally isotrivial      195
Field of invariants of an action      153
Flag manifold      25
Fogarty, J.      193
Fossum, R.M.      267
Freudenthal, H.      42
Frobenius kernels      12
Frobenius morphism      12
Full reducibility      92
Function, additive      63
Function, elliptic      130
Gabriel, P.      12 16 18 51 54 63 64
Gantmakher, F.R.      249 260
Gatti, V      see “Kac V.G.”
Genghis Khan lemma      242
Gieseker, D.      193
Givental’, A.B.      227
Golovina, E.O.      247 258 260
Gorbatsevich, V.V.      207
Gordeev, N.L.      267
Grace, J.H.      267
Graph of an action      154
Grosshans, F.      172
Grothendieck, A.      6 39 59 192 195
Group, $\theta-$       246
Group, additive      10
Group, adele      110
Group, adjoint      244
Group, affine Weyl      103
Group, anisotropic reductive      66
Group, binary polyhedral      143
Group, cofree      239 240
Group, coregular      239
Group, diagonalizable      21
Group, elementary unipotent      63
Group, equidimensional      239
Group, F-      52
Group, general linear      10
Group, isotropic reductive      66
Group, isotropy      14
Group, linear algebraic      9 11
Group, multiplicative      10
Group, nice reductive linear      242
Group, orthogonal      10
Group, polar      246
Group, quantum      13
Group, quasi-simple      37
Group, quasi-split      76
Group, reduced $\theta-$       246
Group, reduced adjoint      245
Group, reductive      28
Group, relative Weyl      68
Group, semi-simple      28

Group, slice-      212
Group, special      159
Group, special linear      10
Group, special orthogonal      10
Group, split reductive      65
Group, split solvable F-      62
Group, symplectic      10
Group, trigonalizable      62
Group, unipotent      20
Group, visible      239
Group, Weyl      27 174 245
Guillemin, V.      227
Gurevich, G.B.      250 258 261
Haboush W.      268
Hajja, M.      268
Hankel determinant      141
Harder, G.      112 117
Harish-Chandra      112 115 116 174 237
Hartshorne, R.      7 140 192 209 217
Hasse principle      118
Helgason, S.      246
Hesselink, W.H.      201
Hessian of a form      146
Hilbert — Mumford criterion      198
Hilbert, D      132 168 169 177 178 181 196—198
Hilbert’s 14th problem      171
Hilbert’s theorem on invariants      168
Hochschild, G.      172
Hochster, M.      176
Hodge, W.V.D.      137 138 255 260
Homogeneous space      14
Homogeneous space, principal      56
Homological dimension of a graded algebra      177
Homomorphism of algebraic groups      13
Humphreys, J.E.      2 23 43 86 87 268
Huneke, C      176
Identity component      13
Igusa, J-i.      190 261 262
Igusa’s criterion      190
INDEX      76 233
Inheritable property      240
Inner form      78
Invariant of a binary form      141
Invariant of a binary polyhedral group      142
Invariant of a group      129
Invariant of a linear operator      134
Invariant of a system of vectors      136
Invariant of a ternary cubic form      145
Invariant of an equivalence relation      129
Invariant of the symmetric group      133
Invariant, basic      143 166
Invariant, integral      130 164
Invariant, j-(of an elliptic curve)      140
Invariant, orthogonal      131 134 136
Invariant, primitive      252
Invariant, rational      130 153
Invariant, regular      164
Invariant, relative      164
Invariant, symplectic      131
Invariant, typical      252
Invariant, unimodular      131 135
Involution, Cartan      92
Isogeny, central      55
Iwasawa decomposition      93 107
Jantzen.J.C.      12 39 45—47
Ja’ja’, J.      268
Jordan decomposition      20
Josefiak, T.      268
Kac, V.G.      224 245—248 262
Kambayashi, T.      149 215
Kasai, S-i.      270
Kats, V.G.      see “Kac V.G.”
Katsylo, P.I.      160—164 220
Kawanaka, N.      246
Kempf — Ness criterion      223
Kempf, G.R.      170 176 180 201 222 243
Kempf’s vanishing theorem      44
Kempken, G.      221
Kernel, semi-simple anisotropic      76
Khadzhiev, D.      173 233
Kimel’fel’d, B.N.      277
Kimura, T.      214 248
Klein, F.      132 142
Kneser-Tits problem      73
Knop, F.      180 181 210 248 250
Kolchin, E.R.      5
Kolmogorov, A.N.      270
Komiya, K.      271
Kostant, B.      222 249 255
Kottwitz, R.      117
Kraft, H.      48 144 146 176 197 198 210 215 219 220 255 261
Kramer, M.      270
Kung, J.P.S.      271
Kunz, E.      176 184 271
Kuribayashi, A.      271
Lang, S.      95 154 158
Lang’s theorem      95
Lascoux, A.      271
Lazard, D.      142 238
Lehrer, G.I.      74 75 100
Lin Tan      171
Littelmann, P.      181 247
Luna, D.      147 194 208—211 213 221 222 229 232 236
MacDonald, I.G.      45
Margulis, G.A.      7 116
Matrix, Cartan      40
Matrix, semisimple      135
Matsushima, Y.      194
Matsushima’s criterion      194
Merzlyakov, Yu.I.      147
Mikityuk, I.V      271
Milne, J.S.      184 217
Miyata, T.      162
Modality of an action      198
Module of covariants      181
Module of covariants, global      183
Module, algebraic A-G-      183
Module, algebraic G-      168
Module, locally strongly efficient      233
Module, slice-      212
Molien, T.      179
Moment mapping      227
Morphism, affine      191
Morphism, etale      209
Morphism, excellent      209
Morphism, finite      191
Mostow, G.D.      176
Muller, I.      271
Mumford, D.      189 192 193 198 243
Mumford’s conjecture      47
Murthy, M.      176
Nagata, M.      170 191
Nakajima, H.      271
Ness, L.      222 227 228
Newstead, P.E.      185 192
Nicolas, J-L.      266
Noether, E.      170 178
Normal form, Weierstrass      145
Null-cone      196
Observable hull      172
Onishchik, A.L.      152 184 193 194 207 246
Operator, averaging      169
Operator, Casimir      47
Operator, polarization      251
Operator, Reynolds      168
Orbit      14 149 151
Orbits, separation of      154
Panyushev, D.I.      215 216 241 243 249
Parshin, A.N.      273
Pauer, F.      273

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