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Bouc S. — Green Functors And G-Sets
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Название: Green Functors And G-Sets
Автор: Bouc S.
Аннотация: This book provides a definition of Green functors for a finite group G, and of modules over it, in terms of the category of finite G-sets. Some classical constructions, such as the associated categroy or algebra, have a natural interpretation in that framework. Many notions of ring theory can be extended to Green functors (opposite Green functor, bimodules, Morita theory, simple modules, centres, ...). There are moreover connections between Green functors for different groups, given by functors associated to bisets. Intended for researchers and students in representation theory of finite groups it requires only basic algebra and category theory, though knowledge of the classical examples of Mackey functors is probably preferable.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 1997
Количество страниц: 342
Добавлена в каталог: 02.12.2009
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of internal homomorphisms 11
of tensor product (first) 15
of tensor product (second) 23
316
29
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196
188
207
209
205
335
-disjoint 188
185
84
218
112
273
278
-perfect 308
307
199
313
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127
181
273
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A-mod 48
a.m 49
Adjunction between and 38
Adjunction between and 148
Adjunction, co-unit 185
Adjunction, unit 185
Algebra associated to a Green functor 84 99 164
Alperin’s conjecture 304
B 52
Balanced 99 154
Bifunctoriality 46 47
Bimodule 141
Bimodule construction 153
Bimodule, structure on 142
Biproducts 68
Biset 167
Biset, composition with 168
Blocks of Mackey algebra 335
Burnside functor as Green functor 55
Burnside functor as initial object 57
Burnside functor as Mackey functor 52
Burnside functor as unit 59
Cartesian product in 109
Cartesian product in 103
Category 186
Category, adding direct summands to a 310
Category, associated to a Green functor 67
Category, equivalence of 79 310—312 314
Category, representation of 71 81
Centre 305
Centre of Yoshida algebra 335
Coinduction 180
Coinflation 168 217
Commutant 143
Commutative Green functor 110 129 305
Commute 136
Composition and associated categories 173
Composition and Green functors 170
Composition and modules 175
Composition and tensor product 168
Composition with a biset 168
Direct summand in 82
Divides in 82
Dual of a module 130
Embedding of algebras 112
Endosimple A-module 304
Equivalence of categories 79 84 112 129 141 155 310—312 314
Equivalence of the definitions of Green functors 48
Examples of algebras 94 95
Examples of composition with a biset 168
Examples of Frobenius morphisms 227
Examples of functors and 215
Examples of functors 332
Examples of Green functors 264
Finitely generated module over a Green functor 114
Frobenius morphisms 223
Functor from G-sets to 68
Functor of evaluation 81
Functorial ideal 291
Functoriality of 147
Functoriality of 177
Functoriality of and 24
Functoriality of 146
G.s.t 229
Generators and relations for 85 88
Generators and relations for the Mackey algebra 7
Green functors and solvable -subgroups 314
Green functors, centre 305
Green functors, composition with a biset 170
Green functors, definition in terms of G-sets 46
Green functors, definition in terms of subgroups 41
Green functors, direct sum 305
Green functors, tensor product 134
G\U.Y 183
Identification of 145
Identification of 320 323 327
Injective on the orbits 177 186 192
Left adjoint and Morita contexts 273
Left adjoint and tensor product 272
Left adjoint to 197
Left adjoint to 183
Lindner construction 94
Mackey algebra 7
Mackey algebra, anti-automorphism 10
Mackey axiom 5
Mackey functors, composition with a biset 168
Mackey functors, definition as modules 7
Mackey functors, definition in terms of G-sets 6
Mackey functors, definition in terms of subgroups 5
Mackey functors, internal homomorphisms 9
Mackey functors, tensor product of 9
Module of finite type 114
Module over a Green functor 41 47
Module over a Green functor, examples 61
Module over the Burnside functor 59
Module, dual 130
Module, right 129
Morita context 100 154
Morita equivalence 99
Morita equivalence of algebras 99 100
Morita Theory 155 160
Morphism of bimodules 141
Morphism of Green functor 41
Morphism of mackey functors 5 6
Morphism of modules over a Green functor 42
Morphism, bilinear 37 127
Morphism, Frobenius 223
Morphism, n-linear 29
Morphism, universal property 29
Multiple of, in CA 82
Natural transformation 316
Non-commutative tensor product 164
Opposite Green functor 127
Product 167
Product 125
Product for 134
Product for 123
Product for 231
Product for 317
Progenerator 115 117 118 155 161 321
Projective G-algebra 292
Projective relative to 102
Projective relative to, solvable -subgroups 314
q(L) 183
Relative projectivity 100
Representation of a category 71 81
Residual rings 274
Restriction 5
Restriction for 15 23
Restriction for 10
Right adjoint to 210
Right modules 129
S.T 229
Same stabilizers 100
Simple Green functors 291
Simple Green functors, classification 295
simple modules 275
Simple modules, classification 276
Simple modules, structure 282
Source algebra 114
Surjective Morita context 154
Tensor product and composition with a biset 168
Tensor product and left adjoints 227
Tensor product and residues 298
Tensor product and right adjoints 242
Tensor product of "algebras" over 164
Tensor product of Green functors 134
Tensor product of Green functors, universal property 137
Tensor product of modules over Green functors 140
Tensor product of simple modules 298
Tensor product, associativity 38
Tensor product, commutativity 38
Tensor product, n-fold 25
Tensor product, n-fold, universal property 29
Thevenaz’s theorem 295
Trace see "Transfer"
TRANSFER 5
Transfer for 15 23
Transfer for 10
U.Y 183
Unitary Green functor 46
Unitary morphism of Green functors 41 43
U[X] 173
Yoshida algebra 95
Yoshida algebra, centre 335
Z(A) 305
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