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Hazewinkel M. (ed.) — Handbook of Algebra, Volume 4
Hazewinkel M. (ed.) — Handbook of Algebra, Volume 4



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Название: Handbook of Algebra, Volume 4

Автор: 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.



In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 518

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Canonical basis      112
Canonical loop      435
Capelli determinant      126 134 135
Capelli-type determinants      135
Cartan homomorphism      58
Cartan map      5 57 69
Cartan matrix      229 351 352 354 356
Cartan matrix of affine type      360
Cartan subalgebra      115 116 121 124 139 159 161
Cartan type      229
Cartan type, braiding      229
Cartan, E.      111
Cartesian power      444
Casimir element      130
Cassidy, P.      243
Categorical dimension      225
Category of algebraic vector bundles      16
Category of finite-dimensional left A-modules      208
Category of finitely generated modules      16
Category of finitely generated projective modules      16
Category of finitely presented R-modules      23
Category of H-comodules      209
Category of locally free sheaves      16
Category of representations      17
Category of smooth quasi-projective varieties      41
Category of vector bundles      17
Category with cofibrations      20
Central multiplicative system      27
Central simple F-algebra      37
Centralizer algebra      113
Centralizer construction      115 153
Cetlin      111
ch-group      477
Chain complex      9
Chamber      445
CHARACTER      117
Character of an order      441
Character, ring      190 222
Character, table      354
Character, theory      197
Characteristic identity      112 116 130 136
Characteristic polynomial      90 270 273
Characteristic polynomial in several variables      276
Characteristic set      256 258 278
Characters of finite reflection groups      340
Charney, R.      445
Cherep, A.A.      469 470
Chern character      6 46 48
Chernikov, group      472 477 479 488
Chernikov, normal divisor      477 478
Chernikov, periodic part      481
Chernikov, S.N.      471 472
Chernikov, Sylow p-subgroup      477
Chevalley group      360
Chevalley property      225
Chevalley, C.      341
CHEVIE      371
Chinese remainder theorem      413
Chow group      6 43
Chow, W.-L.      440
Clark — Ewing classification      376
Class constants      397
Class equation      197
Class equation for finite groups      224
Class equation for semisimple Hopf algebras      223
Class group      6 55 60
Class groups of integers      60
Classical algebraic K-theory      5
Classical braid group      363
Classical dimension polynomial      279
Classical group      394
Classical Lie algebra      111
Classical representation theory      158
Classical semisimple complex Lie algebra      360
Classification of complex reflection groups      341
Classification of Coxeter groups      445
Classification of fibre bundles      8
Classification of finite reflection groups over the quaternions      374
Classification of reflection data      347
Classification of simple Lie algebras      445
Classification of the subgroups of $PSL_2(q)$      404
Classifying space      5 7 14 376 430
Classifying space of a group      8
Classifying space of a small category      8
Clebsch — Gordan coefficients      131
Clifford-theory      370
Co-Morita equivalence      210
Co-Morita equivalent      209
Co-simplicial object      7
Co-simplicial space      7
Coadjoint action      216
Coadjoint orbit      158
Coalgebra      177 455
Coalgebra, map      178
Coassociative      177
Coassociative, up to conjugation      230
Coassociativity      175
Cocommutative      178
Cocommutative element      223
Cocommutative Hopf algebra      182
Cocycle      192 202
Cocycle, condition      191
Cocyclic subgroup      59
Codegrees      343
Coevaluation      209
Coexponents      342
Cofibration      14 20
Cofibration, sequence      20
Cofibration, sequence of exact functors      25
Cofibre of a Cartan map      5
Cofibre sequence of spectra      31
Cofinal      18
Cofinality condition      19
Cohen, F.R.      430 455 458
Cohen, J.      387
Coherent autoreduced set      258
Coherent set of difference polynomials      258
Coherent sheaf      17
Coherently associative      18
Coherently commutative      18
Cohn, R.M.      243 255
Cohomology of braids      430
Cohomology of groups      37
Cohomology of pure braid groups      430
Cohomology of the generalized braid groups      455
Cohomology, theory on Sch      39
Coideal      180
Coideal, subalgebra      221
Coinvariant      186
Coinvariant, algebra      341
Colocal coalgebra      179
Combinatorial diagram      387
Commutative dimension      101
Commutative superalgebra      215
Commutativity      215
Commutativity in a category      215
Commutator subgroup      435
Comodule      180
Comodule, algebra      186 201 205
Comodule, coalgebra      186
Comodule-map      181
Compact complex      23
Compact Lie group      376
Compact Lie group, action      6
Compact object      23
Compatible difference field extensions      304
Complement in a Frobenius group      490
Complement of the discriminant      429
Complete $\sigma$-ideal      262
Complete Abelian subgroup      479
Complete part      479
Complete set of parameters      298 300
Complete subgroup      480
Complete system of $\sigma$-overfields      266
Completely aperiodic      302
Complex conjugation      304
Complex place      35
Complex reflection group      342 348 363 368 374
Composite root      123
Computation of Kolchin polynomials      282
Computer algebra      243
Comultiplication      175 177
Conder diagram      394
Conder, M.D.E.      387 413 414 416
Condition of minimality      489
Condition of minimality for Abelian subgroups      487
Conditions of finiteness      469
Configuration space      429 430 434 443 444 452
Configuration space of a manifold      444
Conflation      15
Conformal field theory      226
Conjugacy class      353
Conjugacy class of Hurwitz groups      405
Conjugacy problem      430
Conjugate biprimitive finiteness      469 471 486
Conjugately biprimitively finite      469 480
Conjugately biprimitively finite group      479 488
Conjugately n-finite      469
Conjugation problem for braid groups      365
Connected coalgebra      179
Connection      198
Connective spectrum      10
Conservative system of ideals      260
Constant      272
Constant element      246
Containing a term      277
Contractible      25
Contragradient of the reflection representation      343
Contravariant inner product      162
Convolution invertible      190
Convolution product      182
Coproduct      20 130 147 455
Coproduct, formula      150
Coquasitriangular      217
Coquasitriangular Hopf algebra      188 190 210 214
Coradical      179
Coradical filtration      180 228
Core of a difference overfield      306
Corepresentation theory for Hopf algebras      185
Coroot      357
Correspondence      41
Cosemisimple      222
Cosemisimple coalgebra      179
Cosemisimple Hopf algebra      182
Cotensor product      181
Cotorsion      36
Cotriangular Hopf algebra      190
Cotriple      12
Counit      177
Counit property      177
Covering      38
Covolume      52
Coxeter braid diagrams      364
Coxeter element      369
Coxeter generator      363
Coxeter graph      349 445
Coxeter group      340 349 356 364 369 430 445
Coxeter matrix      349 352 354 356 369 445
Coxeter presentation      356 374
Coxeter relation      363
Coxeter system      349 356
Cross-product algebra      59
Crossed coproduct      205
Crossed product      193 198
Crystal basis      112
Crystallographic complex reflection group      374
Crystallographic condition      354
Crystallographic group      374
Cup product      35 38
Cyclic cohomology      230
Cyclic multiplier      490
Cyclic quotient      59 60
Cyclotomic extension      40
Cyclotomic polynomial      343
Cylinder axiom      31
Cylinder functor      31
D type pattern      163
D-module      268
Decomposition numbers for $GL_n (\mathbb{F}_q)$      373
Decomposition numbers of $\mathfrak{S}_n$      373
Decorated rooted tree      230
Dedekind domain      27 45 47 55
Dedekind zeta function      51
Dedekind, R.      51
Defining $\sigma$-ideal      252
Defining $\sigma*$-ideal      252
Defining difference ideal      252
Deflation      15
Deformation      217
Deformation, of braids      429
Degeneracy map      7
Degree      92 292
Degree of a difference kernel      292
Degree of a reflection group      341
Degree of transcendence      291
Dehornoy, P.      429 442
Deligne theorem      225
Deligne, P.      445 453
Demazure, M.      375
Dendriform Hopf algebra      230
Density theorem      82
Derivation      102 284
Derivation, ring      87 89
Derived category      5 23
Derived group      413
Descending chain of subgroups      473
Desuspension      41
Devissage Theorem      5 25
Diagonal Cartan subalgebra      139
Diagonalizable      340
Diagram automorphism      365
Dickson classification of subgroups of $SL_2(q)$      412
Dickson classification of the subgroups of $PSL_2(q)$      404
Difference, $\sigma$-polynomial      270
Difference, algebra      243 290
Difference, algebraic equation      252
Difference, automorphism      247
Difference, dimension      271
Difference, dimension, polynomial      270
Difference, dimension, polynomial, of the module associated with the p-dimensional filtration      279
Difference, domain      312
Difference, endomorphism      247
Difference, equation      286
Difference, factor ring      247
Difference, field      245
Difference, field, extension      245
Difference, Galois group      314 315 326 329
Difference, Galois theory      329
Difference, homomorphism      247 269 316
Difference, ideal      245
Difference, indeterminates      250
Difference, isomorphism      247
Difference, kernel      39 291
Difference, kernel of length r      294
Difference, operator      268
Difference, overring      245
Difference, place      312
Difference, quotient field      313
Difference, quotient ring      247
Difference, R-module      268
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