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Lorenz M. — Multiplicative Invariant Theory
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Название: Multiplicative Invariant TheoryАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2005Количество страниц: 177Добавлена в каталог: 12.05.2008Операции: Положить на полку |
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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 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 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, 36 G-lattice, 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, 36 G-module, 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, 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 90 93 Multiplicalive invariants of 58 70 Multiplicalive invariants of 62 63 Multiplicalive invariants of 57 Multiplicalive invariants of 122 Multiplicalive invariants of inversion 57 Multiplicalive invariants of rank 2-lattices 60 153 Multiplicalive invariants of the 58 Multiplicalive invariants of the 122 Multiplicalive invariants of the 121 Multiplicalive invariants of the diagonal subgroup of 55 Multiplicalive invariants of the diagonal subgroup of 57 Multiplicalive invariants of the Klein group 59 Multiplicative group 66 Multiplicative invariant algebra 1 Multiplicative invariant field of 140 Multiplicative invariant field of 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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