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Hazewinkel M. (ed.) — Handbook of Algebra, Volume 4
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Название: Handbook of Algebra, Volume 4Автор: Hazewinkel M. (ed.) Аннотация: Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 518Добавлена в каталог: 30.06.2008Операции: Положить на полку |
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Предметный указатель
Difference, ring 244 Difference, specialization 312 Difference, subring 245 Difference, transcendence basis 280 Difference, type 271 282 Difference, valuation 312 Difference, valuation, ring 312 Difference, vector space 268 Difference-differential dimension polynomial 285 Differential 284 Differential algebra 243 Differential dimension polynomial 285 Differential equation with delay 244 Differential field 284 Differential form 454 Differential Galois theory 243 Differential operator 80 86 Differential polynomial 253 Dihedral group 6 58 192 361 481 482 DIMENSION 271 Dimension of a 290 Dimension of a variety 297 Dimension of an ideal 297 Dimension, polynomial 285 Dimension, theory of differential rings 243 Discrete G-module 36 Discrete orbit category 64 Discrete torsion group 40 Discrete valuation ring 27 46 Discrete-time nonlinear systems 244 Discriminant 365 429 Discriminant of a reflection group 365 Distinguished grouplike element 195 Division algebra 55 Divisor map 49 Doi — Hopf module 214 Domination 312 Double centralizer theorem for Lie color algebras 221 Double crossed product 193 Double crossproduct 200 216 Dress, A. 6 57 Drinfeld, double 190 193 213 216 Drinfeld, element 189 226 Drinfeld, generator 116 136 Drinfeld, map 189 Drinfeld, V.G. 158 188 Dual bases 209 217 Dual characteristic identity 132 Dual cocycle 202 Dual Hopf 2-cocycle 191 Dual Hopf algebra 184 Dual partition 370 Dual projection operator 132 Dual pseudo-cocycle 192 Dual representation 398 Dual root system 357 Dwyer and Friedlander 6 Dwyer, W. 46 Dynkin diagram 355 Effective order 296 Effective order of a 296 Effective order of a 296 Effective order of a variety 297 Effective order of an ideal 297 EI category 6 63 Eichler order 6 61 Eichler, M. 61 Eilenberg — MacLane space 11 363 Eilenberg — MacLane spectrum 11 Elementary matrix 413 Enough injectives 37 39 Enright — Varadarajan module 137 Enveloping algebra 83 89 111 175 228 Enveloping algebra of a Lie color algebra 218 Enveloping algebra of a Lie superalgebra 218 Epimorphic images of triangle groups 391 Equalizer diagram 39 Equation in finite differences 286 Equivalent 307 Equivalent filtrations 82 Equivalent realizations 295 Equivalent tuples 252 Equivariant higher algebraic K-theory 6 Equivariant higher K-theory 5 65 Equivariant homotopy equivalence 453 Equivariant Reidemeister torsion 63 Essential prime divisor 261 264 291 Essential separated components 265 Essential separated divisors 263 Essential strongly separated divisors 263 Etale, Chern character 46 51 Etale, cohomology 5 6 34 38 46 Etale, cohomology, group 6 Etale, hypercohomology 39 Etale, K-theory 6 Etale, mapping 39 Euclidean plane 389 Euclidean structure 444 Euclidean triangle 388 Euler totient function 414 Evaluation 209 Exact category 5 15 65 Exact category in the sense of Quillen 64 67 Exact connected sequence of functors 24 Exact filtration 269 273 Exact p-dimensional 277 Exact pairing 66 Exact sequence 66 Exact upper bound for the Gelfand — Kirillov dimension 104 Exceptional complex reflection group 372 Exceptional group 348 445 Exceptional Lie algebra 111 Exceptional Lie algebra, 136 Exceptional simple group of Lie type 397 Exceptional Weyl group 372 Exchange condition 350 Excision 32 Excision, ideal 33 Exhaustively and separately filtered module 269 Existence theorem 298 EXPONENT 226 341 343 369 Exponent of an irreducible character 343 Exponent of Hopf algebras 226 Ext functor 273 Extended Mickelsson algebra 122 Extension 193 Extension, axiom 21 Extension, of the twisted Yangian 138 Exterior algebra 44 Extraordinary cohomology theory 10 Extremal projector 112 116 121—123 139 159 Extreme group 477 F*-condition 473 F*-group 474 F-group 474 Face map 7 Factorizable 217 Factorizable Hopf algebra 190 Factorization theorem for matrices 404 Faddeev, L.D. 115 158 Fadell, E. 430 446 452 453 Faithfully flat H-Galois extension 201 Fake degree 342 369 372 Fenn, R. 431 448 450 Fiber 211 Fiber, bundle 8 452 Fibration 364 452 Field of invariants 375 Filter dimension 79 81 83 87 Filter dimension of a polynomial algebra 83 Filter inequality 80 97 Filtered 268 Filtered 268 Filtration 273 Finite complex reflection group 368 374 Finite Coxeter group 356 373 Finite Coxeter system 349 Finite difference 270 Finite filtration 25 Finite fusion category 231 Finite general linear group 373 Finite generation of Gn (?) 29 Finite generation of K-groups 44 Finite group of Lie type 343 Finite groups generated by reflections 339 Finite length 93 Finite reductive group 343 Finite simple group 387 Finite tor-dimension 24 Finite type Coxeter group 349 Finite Weyl group 361 373 Finite-dimensional Kac-Moody algebra 360 Finite-dual 184 Finitely approximate 474 Finitely embedded 488 Finitely embedded involution 488 Finitely generated 246 Finitely generated 268 Finitely generated 247 Finitely generated 247 Finitely generated 246 Finitely generated difference algebra 290 Finitely generated difference overring 247 Finitely generated difference ring extension 247 Finitely generated inversive 247 Finitely generated inversive 247 Finitely generated inversive difference overring 247 Finitely generated inversive difference ring extension 247 Finitely generated type 290 Finitely partitive 85 95 Finitely partitive algebra 100 Finitely partitive K-algebra 89 Finiteness conditions 469 Finiteness results 6 First filter inequality 79 Flasque category 25 Flat 39 Flat, A-module 24 Flip 178 210 Formal series 122 Fox, R. 430 444 Franke, C 321 free 249 Free 277 Free Burnside group 484 487 Free filtered 274 Free group 364 413 429 434 Free join 294 Free left D-module 277 Free simplicial ring 10 Friedlander, E. 46 Frobenius, algebra 195—197 Frobenius, automorphism 34 Frobenius, F.G. 400 Frobenius, formula 408 Frobenius, group 481 484 488 490 491 Frobenius, map 343 Frobenius, pair 490 Frobenius, property 219 Frobenius, theorem 224 490 Frobenius, theory 373 Frobenius, type 224 226 FRT construction 212 213 Fuchsian group 389 390 394 Fuks, D.B. 430 455 Full difference Galois group 318 Full Galois group 320 Full group 317 Functional equation 244 Fundamental domain 390 Fundamental Galois theorem for PVE 317 Fundamental group 429 Fundamental matrix 324 Fundamental representation 158 Fundamental system of solutions 316 Fundamental theorem for G-theory 31 Fundamental theorem for Hopf modules 197 219 Fundamental theorem of higher K-theory 30 Fusion category 177 231 G-graded algebra 204 G-space 8 G-spectrum 6 G-theory 5 31 56 58 G-torsor 327 G/G exact 67 G/H -exact 67 Gabriel, P. 79 102 Galois, closed 317 319 Galois, closed field 317 Galois, closed subgroup 317 Galois, cohomology 5 34 Galois, cohomology, group 40 Galois, correspondence 318 Galois, correspondence for total Picard — Vessiot rings 329 Galois, extension 203 Galois, map 201 203 Galois, object 201 204 Galois, theorem for PVE 317 Galois, theory 197 201 401 Galois, theory of difference equations 323 Galois, type correspondence theory 208 Garside left normal form 440 Garside right normal form 440 Garside, F.A. 429 430 440 Gauge equivalence 224 Gauss, C.-F. 429 Gelfand — Kirillov dimension 79 81 86 97 98 102 Gelfand — Kirillov transcendence degree 102 Gelfand — Tsetlin, basis 116 118 131 134 164 Gelfand — Tsetlin, formula 111 112 Gelfand — Tsetlin, integrable system 158 Gelfand — Tsetlin, module 137 Gelfand — Tsetlin, module over the orthogonal Lie algebras 164 Gelfand — Tsetlin, pattern 114 118 136 Gelfand — Tsetlin, pattern for the B,C and D types 142 Gelfand — Tsetlin, subalgebra 135—137 Gelfand — Tsetlin, type basis 115 136 148 Gelfand — Weyl — Zetlin basis 165 Gelfand — Zetlin module 165 Gelfand, I.M. 111 General linear group 373 General linear group over a finite field 372 General linear Lie algebra 111 116 General polynomial 429 General position 147 Generalized braid group 430 444 Generalized Chernikov group 479 480 Generalized Chernikov periodic part 481 Generalized cohomology theory 10 Generalized Liouvillian extension 321 Generalized Picard — Vessiot extension 319 Generalized quaternion algebra 411 Generalized quaternion group 59 485 Generating subspace 93 94 Generator of the monodromy around H 362 Generic prolongation 291—295 Generic representation 136 Generic solution field 319 321 Generic specialization 293 297 Generic zero 252 265 291 297
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