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Lorenz M. — Multiplicative Invariant Theory
Lorenz M. — Multiplicative Invariant Theory

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Название: Multiplicative Invariant Theory

Автор: Lorenz M.

Аннотация:

Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 177

Добавлена в каталог: 12.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathbb{Z}$-structure      52
(G, H) -section      142
Action by linear substitutions of the variables      2
Action, exponential      1
Action, fixed-point-free      118 153
Action, lattice      1
Action, linear      2 86
Action, monomial      1
Action, multiplicative      1 52
Action, purely monomial      1
Action, twisted multiplicative      1 64
Affine semigroup      54
Affine semigroup, normal      54 85 151
Affine semigroup, positive      55
Algebra of polynomial functions      127
Algebra of rational functions      127
Algebra of vector invariants      123
Algebraic group      155
Algebraic line bundle      78
Algebraic torus      65 66 100 133
Antipode      66
Antisymmetric tensors      17
Augmentation      14 43 66 77 80 111 152
Augmentation, ideal      84 97 100
Automorphism group      25
Bardsley, P.      97
Barge, J.      65 139
Base of a root system      25
Bass, H      77
Beneish, E.      5 6 33 43 47 50 139 146 159 160
Benson, D.      70
Bergman — Roseblade Theorem      4
Berhuy, G.      155
Bessenrodt — Le Bruyn stable rationality theorem      6
Bessenrodt, C      5 6 33 34 47 146
Binary icosahedral group      119 121
Bireflection      120
Bireflection group      55
Bireflection on a lattice      103
Bireflection on a ring      73 116
Bireflections      149
Bogomolov, R      139 160
Bourbaki      4 27 149
Bourbaki’s theorem      6 51 61 96
Buhler, J.      155
Carat      3 28 30
CHARACTER      17
Character group      67 144
Character lattice      144 156
Chinese remainder theorem      83
Chu, H.      160
Chuang, C.      97
Class group      69—75 152
Class of a linear group      21
Cocycle      80
Coflasque resolution      37
Cohen — Macaulay problem      103 154
Cohen — Macaulay property      3 85 90 103—123
Cohen — Macaulay, module      106
Cohen — Macaulay, ring      106 154
Colliot — Thelene, J.L.      5 6 33 34 36 40 42 43 49 78 135 139 146
Compression      155
Comultiplication      66
Congruence subgroup      24
Constructive Galois theory      5
Cortella, A.      50
Counit      66
Cup product      114
Dade, E.      30
Decomposition group      83 97
DeMeyer, F.      126
Depth      105
Derksen, H.      154
Direct sura      16
Discrete valuation domains      71
Dolgachev, I.      131
Donkin, S.      143
Eagon, J.      107 108
Eckmann — Shapiro Lemma      36 40 41 120 121
Effective quotient      20 62 88 89 99
Elementary symmetric function      58 140
Ellingsrud — Skjelbred spectral sequences      7 110—112 115
Ellingsrud, G.      104 110
Endo, S.      33 34 42 135
Essential dimension      155
Essential dimension, estimates for $PGL_n$      157
Exponential invariants      4
Exterior power      16
Farkas, D.      1 6 27 85 95 96 139
Favi, G.      155
Field extension      125
Field extension, rational      4 125
Field extension, retract rational      126 128—131
Field extension, stably rational      126
Field extension, unirational      126
Finite representation type      19
Fischer, E.      160
Flasque equivalence      38—39 135
Flasque resolution      37
Formanek, E.      5 33 44 143 146 148 159
Formanek’s rationality theorems      6
Friedland, S.      31
Frit, W.      31
Frobenius reciprocity      18
Function fields of algebraic tori      133
Fundamental dominant weights      26
Fundamental invariants      87
Fundamental theorem for $S_n$-invariants      58 88
Fundamental weights      26 61 89
G-action, twisted multiplicative      132
G-fleld      125
G-fleld, (twisted) multiplicative      127 132 143
G-fleld, faithful      125
G-fleld, linear      127
G-fleld, multiplicative      1
G-fleld, twisted multiplicative      1
G-lattice      1 13
G-lattice, $\hat{H}^i$-trivial      36
G-lattice, $\Pi^i$-trivial      40
G-lattice, coflasque      36 37
G-lattice, dual      17
G-lattice, effective      13 20 62 93 117
G-lattice, faithful      13
G-lattice, flasque      36 37
G-lattice, free      15
G-lattice, indecomposable      18
G-lattice, induced      18
G-lattice, invertible      35
G-lattice, monomial      40 133
G-lattice, permutation      14 17 33—34 133
G-lattice, permutation projective      35
G-lattice, permutation, stably      34
G-lattice, projective      15
G-lattice, quasi-permutation      39 133 135
G-lattice, rationally irreducible      14 150
G-lattice, regular      15 127
G-lattice, self-dual      17 18 33
G-lattice, trivial      13
G-module      13
G-module, $\hat{H}^i$-trivial      36
G-module, $\Pi^i$-trivial      40
G-module, rationally irreducible      14
G-ring      64
G-variety      141
G-variety, generically free      155
Galois descent lemma      67 131
Gap      3 30 78 96 123 154
Gaschutz, W.      160
Generic division algebra      143 159
Generic polynomial      126 133 155 160
Genus      14
Gobel, M.      154
Gordeev, N.      21 73
Grade      105
Grade of an ideal      105
Grade of an ideal on a module      105
Grothendieck group      35 119
Grothendieck spectral sequence      110—111
Grothendieck, A.      110
Group algebra      51
Group of prime order      19
Group, crystallographic      4
Group, Klein      43 59
Group, lineaily reductive      98
Group, metacyclic      19 42
Group, polycyclic-by-finite      4
Group, quaternion      43
Group-like element      66
Guba, V.      22
Gubeladze’s theorem      86
Gubelaze, J.      151
Guralnick, R.      149
Hajja, M.      5 134 139 140 148 159
Height      73 104
Hilbert basis of a monoid      55 90 93 151
Hilbert’s Theorem      90 72 83 132 137
Hochster, M.      85 107 108 151
Hopf algebra      2 66
Huffman, W.C.      122 149
Humphreys, J.      27
Indecomposable element of a monoid      90
Indecomposable G-lattice      18
Inertia group      72 73 81 112 115
Integrally closed domain      77
Invariant basis lemma      131
Invertible module      77 78
Isotropy group      20 33 104
Jordan number      31
Jordan’s Theorem      3 28
k-reflection      73 115 153
Kac — Moody algebra      4
Kang, M.-c.      5 78 83 134 139 140 148 159 160
Katsylo, P.      5 142 148
Katznelson, Y      31
Kemper, G.      73 104 109 123 154 155
Knop, K.      97
Krull domain      69—72 77
Krull — Schmidt theorem      19
Kuniyoshi, H.      160
Kunyavskii, B.      50
Lattice      1 13
Laurent polynomial algebra      52
Le Bruyn, L.      5 6 33 34 47 127 143 146
Leading coefficient      92
Leading exponent      92
Leading monomial      92
Leading term      92
Lee, P.      97
Lemire, N.      5 27 44 47 50 140 157 158
Lemire’s theorem      140
Lenstra, H.      5 126 127 135
Levy, L.      160
Lexicographic order      92
Linearization      65 97
Local cohomology      106
Localized polynomial algebra      126
Locally isomorphic lattices      14
Lomakina, Z.      30
Lorenz, M.      44 47 50 156 158
Luna’s slice theorem      3 97
m-sequence      105
Mackey decomposition theorem      18
Magma      30 154
Masuda, K.      132
McKenzie, T      126
Merkurjev, A.      155
Minkowski bound      31
Miyata, T.      33 34 42 132 135 160
Moduli space      159
Monoid, $\Phi$-simplicial      151
Monoid, affine normal      54 151
Monoid, cancellative      54
Monoid, positive      55
Monoid, torsion-free      54
Monomial order      53 92
Monomials      52
Morita equivalence      131
Multiplicalive invariants of $A_2$      90 93
Multiplicalive invariants of $A_{n-1}$      58 70
Multiplicalive invariants of $A_{n-1}*$      62 63
Multiplicalive invariants of $B_n$      57
Multiplicalive invariants of $S_n$ -lattices      122
Multiplicalive invariants of inversion      57
Multiplicalive invariants of rank 2-lattices      60 153
Multiplicalive invariants of the $S_n$-lattice $U_n$      58
Multiplicalive invariants of the $\mathcal{A}_n$-lattice $A_{n-1}$      122
Multiplicalive invariants of the $\mathcal{A}_n$-lattice $U_n$      121
Multiplicalive invariants of the diagonal subgroup of $GL_n(\mathbb{Z})$      55
Multiplicalive invariants of the diagonal subgroup of $SL_n(\mathbb{Z})$      57
Multiplicalive invariants of the Klein group      59
Multiplicative group      66
Multiplicative invariant algebra      1
Multiplicative invariant field of $Aut(A_{n-1})$      140
Multiplicative invariant field of $W(A_{n-1})$      139
Murthy, M.P.      77
Nakajima, H.      3 86
Nebe, G.      28 30
no-name lemma      131 159
Noether problem      4 125 126 159
Noether, E.      4 125
Noether’s finiteness theorem      53 96 108 136
Norm      14 42
Ojanguren, M.      139
Oliver, R.      35
Orbit sum      2 52
Panyushev, D.      151
Patliak, J.      123 150
Permutation class group      35
Picard group      77—84
Plesken, W.      31
Polynomial invariants      2 78 86 97
Polynomial invariants, Picard group of      83
Popov, V      5 89 142 143 158
Primary invariants      154
Principal divisors      71
Procesi, C.      5 143 146
Projective class group of an order      35
Pseudo-reflections      21
Quillen — Suslin theorem      96 107
quiver      159
R#G-module, canonical      79
Ramification index      71
Rational functions      141
Rational map      141
Rational map, domain of definition of      141
Rational map, indeterminacy locus of      141
Rational quotient      141
Rational type      14 117 151
Rationally isomorphic lattices      14 17 65 117 140 150
Raynaud, M.      98
Reduced root system      24
Rees, D.      105
Reflection      7 21 69 74
Reflection group      21 55 96 99 100
Reflection group, generalized      21
Reflection group, k-      21
Reflection subgroup      27 69
Reflection, bi-      7 21 103 120 149
Reflection, diagonalizable      23 69 88 89
Reflection, generalized      21 73 115 149 153
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