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Neusel M.D. — Invariant Theory of Finite Groups
Neusel M.D. — Invariant Theory of Finite Groups

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Название: Invariant Theory of Finite Groups

Автор: Neusel M.D.

Аннотация:

The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 371

Добавлена в каталог: 28.11.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Example, $\mathbb{Z}/2\times\mathbb{Z}/4$      56
Example, $\mathbb{Z}/3$      38 64 223
Example, $\mathbb{Z}/4$      7 39 43 147 223
Example, $\mathbb{Z}/6$      224
Example, $\mathbb{Z}/6\times|\mathbb{Z}/2$      226
Example, $\mathbb{Z}/k$      46 50 213 216
Example, $\mathbb{Z}/m$      208
Example, $\mathbb{Z}/p$      65 161 173
Example, $\mathbb{Z}/p\times\mathbb{Z}/p\times\mathbb{Z}/p$      164
Example, $\mathbb{Z}4\times|\mathbb{Z}/2$      226
Example, $\mathbf{D}(2)$      80
Example, $\mathrm{GL}(2,\mathbb{F}_{p})$      80 213
Example, $\mathrm{PSL}(2,\mathbb{F}_{q})$      230
Example, $\mathrm{SL}(2,\mathbb{F})$      230
Example, $\mathrm{SL}(2,\mathbb{F}_{p})$      213
Example, $\mathrm{SL}(2,\mathbb{F}_{q})$      104
Example, $\mathrm{SL}(n,\mathbb{F}_{q})$      273
Example, $\mathrm{SL}_{k}(2,\mathbb{F}_{p})$      213
Example, $\mathrm{Syl}_{p}(\mathrm{GL}(2,\mathbb{F}_{p})$      215
Example, $\mathrm{Uni}(2,\mathbb{F}_{p})$      215
Example, $\mathrm{Uni}(n,\mathbb{F}_{q})$      110
Example, $\mathrm{Up}(2,\mathbb{F}_{p})$      216
Example, $\mathscr{I}$      54
Example, $\mathscr{Q}_{4k}$      131
Example, $\mathscr{Q}_{8}$      82 94 98 216 274
Example, $\mathscr{Q}_{n}$      173
Example, $\Sigma_{3}$      9 225
Example, $\Sigma_{n}$      5 35
Example, alternating group      5
Example, dihedral group      82
Example, Frobenius group      280
Example, orthogonal groups      308
Example, special orthogonal groups      308
Example, Stong's      164
Example, symmetric group      5
Examples, $\mathbb{Z}/m$      207
Excess      237
Exponent sequence      69
Extended ideal      8
Extension      268
Exterior algebra      116
E[V]      116
Factorial      25
Faithful      5
Feshbach's transfer theorem      40 42 169 268
Feshbach, M.      171
Field of fractions      25 26 105 106 107 242
Fine Chern classes      91 92
Fine orbit Chern classes      16 98
Finite extension      31
Finite length      118
Finite p-group      102 103
Finite symplectic group      276
Finite type      45 316
Finite, noetherian      14
Finiteness, algebraic      12
Finiteness, combinatorial      14
Finiteness, homological      13
First Fundamental Theorem      25
First Main Theorem of Invariant Theory      86
Fixed point freely      11
Fixed-point set      173
Flag      164
Flag of subspaces      110
Flat      320
Forms      2
Forms, as functions      3
Fractal of the Dickson algebra      270 278
Fractal property      155 271
Fractal property of the Dickson algebra      271
Fractal property of the Steenrod algebra      271
Free R-module on a set      57
Freyd's adjoint functor theorem      284
Frobenius homomorphism      21 227
Frobenius map      271
Frobenius subgroup      280
Fundamental class      124 194
Fundamental theorems      24
G-invariant configuration      103
G-set      57
G-stable      6
Galois embedding theorem      245
Galois field      2
Generalized Landweber — Stong conjecture      254
Generalized quaternion group      131 173
Generalized quaternion groups      217
Global dimension      118
Global dimension d      118
Goebel's bound      74 149
Goebel's Theorem      46 69 73
Goebel, M.      18
Going down      323
Going up      323
Good primes      187
Gorenstein      54 213
Gorenstein ring      146
Gorenstein rings      143
Graded algebra      316
Graded algebra of maps      287
Graded algebra of polynomial functions      2
Graded complete intersection      68
Graded field      105
Graded field of fractions      105 317
Graded module      317
Graded vector space      316
Grading, negative      248
Gradings      315
Grassmann variety      269
Group action      1
Group algebra      6
Group of odd order      27
Height      42
Herbrand's lemma      178
Higher center      209
Higher-order differential operator      229
Hilbert function      14
Hilbert ideal      9 167
Hilbert — Serre theorem      66 67
Hilbert's basis theorem      1 30
Hilbert's Nullstellensatz      1 326
Hilbert's syzygy theorem      1 118
hom-codim(-)      139
hom-dim-(-)      118
Homological algebra      13
Homological codimension      19 129 173
Homological degree      116
Homological dimension      118
Homological finiteness      13
Homological properties      278
Hopf algebra      231
Hyperplane      156 186
Hyperplane of a pseudoreflection      186
Hyperplane of a transvection      156
Hypersurface      146 310
Icosahedral group      54 191 220
Ideal of stable invariants      11
Ideal, maximal      322
Ideal, primary      322
Idempotent      294
Ifp-basis      102
Ifp-dimensions      102
Imbedding property      242
Imbedding theorem      245 270 278 291
Indecomposable elements      318
INDEX      33
Index sequence      234
Injective hull      247 248 251
Integer representation      221
Integral extension      31 320
Integral extensions and the functor T      292
Integrally closed      25
Internal degree      117 174
Intertwining action      287
Invariant ideal      23 259 260
Invariant ideals      23
Invariant prime ideal spectrum      266
Invariants of $\mathbb{Z}/p$ in characteristic p      160
inverse invariant theory problem      22
Irreducible ideal      143
Irreducible representation      75
Irredundant primary decomposition      322
Isolated prime      322
Isometries of a square      82
Isometries of the square      127
Isotropy group      35 57 60
Isotropy subgroup      75 308
Isotypic component      6
Iterated fixed-point filtration      101
Iterated fixed-point length      101
Iterated fixed-point set      101
Ith polarized Chern class      87
Ith polarized elementary symmetric polynomial      87
Jacobian determinant      126 194
Jordan block      161
Jordan canonical form      160
Kaehler differentials      303
Koszul complex      114 116 117 173 250
Koszul complex, modified      178
Koszul's Theorem      117
Krull dimension      25 42 115 324
Krull dimension and the functor $\mathrm{T}$      292 297
Krull relations      268 320 322
Kth doubly polarized Chern class      91
Lam's $\mathcal{J}$-construction      260
Landweber — Stong conjecture      246 247 283
Landweber's Theorem      270
Landweber, P.S.      158
Lannes — Zarati structure theorem      249
Lannes's $\mathrm{T}$-functor      284
Lasker — Noether Theorem      1 268 322
Leibniz rule      35
Length      234
Local cohomology      176
Local cohomology spectral sequence      176
Lying over      323
Lying-over      271
Macaulay's theorem      278
Maximal      322
Maximal ideal      322
Maximal regular sequence      129
Minimal polynomial      203
Minimal resolution      121
MOD/A      118
Modified Koszul complex      178
Modular case      2
Modular invariant theory      151
Module of indecomposable elements      120
Molien's theorem      46 49
moment      234
Monic polynomial      31
Monomial      3
Monomial basis      59
Moore, J.C.      315
Morphism of degree d      316
Multiindex      3
Multiplicity      6 63
Multiplicity function      63
Multipolarized Chern classes      91 92
Multipolarized elementary symmetric polynomials      92
Multiset      63
n-fold Cartesian product      61
Nakajima — Stong Theorem      109
Nakajima's Theorem      307
Nakajima, H.      159 164
Nakayama's lemma      318
Negatively graded      248
Newton's formula      81
Nilpotent group      210
Nilpotent groups      23
Nilradical      255
Noether map      29 85
Noether normalization      324
Noether Normalization Theorem      14 323
Noether problem      26
Noether's bound      17 36 149
Noether's finiteness theorem      31
Noetherian      25
Noetherian finiteness      14
Noetherian module      30
Noetherian ring      30
Noetherianess      290 291 294
Nonassociates      27
Nondiagonalizable pseudoreflection      156
Nonmodular case      2
Nonnegatively graded      45
Norm      79
Normal extension      323
Octahedral group      220
Optimal system of parameters      18
Orbit      1 57
Orbit Chern classes      16 78 255
Orbit polynomial      78
Orbit sum      58
Orbit sums      58
Order of the pole      69
Orthogonal group      308 309
P(M,t)      45
p-group      27 210
p-groups      23 152 160 193
p-Sylow subgroup of $\mathrm{GL}(n,\mathbb{F}_{q})$      110
p-Sylow subgroup of $\mathrm{SL}(n,\mathbb{F}_{q})$      110
Palindromic polynomial      145
Parabolic Group      216
Parameter ideal      143
Permutation invariants      69
Permutation representation      8 17 23 46 57 149
Pigeonhole Principle      207
Poincar series      46
Poincar'e duality algebra      194
Poincar'e series      67
Poincare duality algebra      124 126
Poincare series      14 45 57 59 66
Pointwise stabilizer      20 146 192 283 288 289 307
Polar axis      54 191 192
Polarized Chern classes      213
Polarized elementary symmetric polynomials      87
Poles      54
Polynomial algebra      2 146 164
Polynomial algebra problem      19
Polynomial algebras and the $\mathrm{T}$-functor      302
Polynomial functions      2 4
Positively graded      45
Pre-Euler class      104 213 267
Primary decomposition      320
Primary ideal      322
Prime avoidance lemma      320
Prime field      49
Prime Filtration Lemma      330
Prime ideal spectrum      259
Primitive derivation      244
Principal ideal      35
Proj(-)      259
proj-dim_(-)      118
Projective      10 320
Projective dimension      18 25 118
Projective resolution      13 174
Pseudo-optimal      18
Pseudoreflection      51 124 186
Pseudoreflection group      186 193
Pseudoreflection groups      186 194
1 2 3
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