Gracia-Bondia J.M., Varilly J.C., Figueroa H. — Elements of Noncommutative Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Gracia-Bondia J.M., Varilly J.C., Figueroa H. — Elements of Noncommutative Geometry

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Название: Elements of Noncommutative Geometry

Авторы: Gracia-Bondia J.M., Varilly J.C., Figueroa H.

Аннотация:

The subject of this text is an algebraic and operatorial reworking of geometry, which traces its roots to quantum physics; Connes has shown that noncommutative geometry keeps all essential features of the metric geometry of manifolds. Many singular spaces that emerge from advances in mathematics or are used by physicists to understand the natural world are thereby brought into the realm of geometry." "This book is an introduction to the language and techniques of noncommutative geometry at a level suitable for graduate students, and also provides sufficient detail to be useful to physicists and mathematicians wishing to enter this rapidly growing field. It may also serve as a reference text on several topics that are relevant to noncommutative geometry.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 685

Добавлена в каталог: 06.05.2005

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Предметный указатель

-cycle      483 489
-cycle, reduced      403 405 SOS
-cycle, unreduced      401
cofunctor      101
functor      165
-spinors      389
structure      382
$\delta$ -invariant functional      636 637
$\Gamma$ functor      57 59 370
$\mathbb{Z}_2$ -grading      174 210 371
$\mathcal{A}$ -bimodule      81 320
$\mathcal{A}$ -linear map      79
$\sigma$ -compact space      15
$\sigma$ -trace      636
(1, 1)-periodicity      177 402
*-homomorphlsm      10 12 136
4-vector      558
A-compact operator      71 84 89 146
A-compact projector      86
A-flnite rank module      91
A-flnite Tank operator      71
A-Fredholm operator      146 164
Absolute value of an operator      310
Action functional      270 492 507
Acydic complex      344 353 358 433
Adjoint      14 70 393
Adjointahle operator      70 84
AF-algebra      96 129 532
Afflne connection      254
Alexander — Spanier cobomology      325
Algebra of classical symbols      267 349
Algebra of rooted trees      602 614
Algebraic if-theory      94 131
Algebraic tensor product      32
Amplitude      298
Annihilation operator      122 187 427
Anomalous commutator      222
Anticommutation relation      173
Anticommutation relation, canonical      241
Anticommutator      173 328
Antiderivation      211
Antipode      39 606 634
Antipode, twisted      636
Antiskew operator      200 217 239
Antlunitary operator      189 399 481 505
Approximate unit      29 65 497
Arc length      390
Asymptotic expansion      118 275
Asymptotic morphism      110 130
Asymptotic morphism, Moyal      120 122
Attachment      21 109
Augmentation      153
Augmented algebra      136
Automatic continuity      12
Automorphism      15 523
Automorphism Bogoliubov      174 181 214
Automorphism group      11
Banach algebra      4 27 135 448 469
Banach algebra, involutive      6 27 138
Banach module      69
Banach space      312
Banach — Lie group      221 225
Banach-space interpolation      317 467
Bar resolution      353 362 433
Berezin integral      203 479
Berezin quantization      201
Bereztn — Patodi formula      203
Bialgebra      36 399
Bianchi identity      256 339
Bicommutant      483 542
Blmodule      81 599
Blvector      182
Bochner — Weltzenbdck formula      396
Bockstein homomorphism      19
Bogoliubov automorphism      174 161 214 232 378 488
Borel — Weil construction      420
Bore] functional calculus      129
Bott element      122 133 189
Bott map      124
Bott periodicity      189
Bott projector      77 122 514
Bra operator      378
Branch of a rooted tree      601
Bratteli diagram      96
Brouwer degree      77
Bubble diagram      585 592
Bundle equivalence      50 53 55
Bundle map      50 370
Bundle morphism      52 505
Butcher group      617
C* -bundle      158
C* -module      65 83 159 189
C* -module, full      65 159
C* -module, selfdual      73
C*-algebra      4 27 523
C*-algebra, $\sigma$ -unital      15 29 148 157
C*-algebra, contractible      16 23
C*-algebra, elementary      167
C*-algebra, nonunital      14 97 128
C*-algebra, nuclear      33
C*-algebra, simple      214 529 538
C*-algebra, stable      85
C*-algebra, transformation group      524 550
C*-bimodule      160
C*-cross-norm      24
C*-dynamical system      523
C*-inductive limit      96 99 532
C*-norm      4 24 65 84 524
Calderon's formula      144 243
Calkin algebra      133 141
Cancellation semigroup      95
Canonical anticommutatlon relations      241
Cartan an subalgebra      420
Cartan identity      253 265 361
Cartesian product      23 •
Cauchy integral formula      134
Cauchy principal-value integral      330
Cayley's counting formula      608 615
Cech cocycle      19 50 374
Cech cohomology      18 50 325 378
Cell complex      108 420 539
Central extension      181 194 223 236
Cesaro mean      286 474
Cesaro order at infinity      275
Chain homotopy      344 431
Chain map      344 362
CHARACTER      5 617 630 636
Character of a cycle      350 352
Characteristic map      639
Charge      238
Charge anomaly      243
Charge conjugation      175 181 191 399
Charge, quantized      242
Charged field      238 328 576
Charged vacuum      244
Chern character      339 340 350 441 445 447 450 470 493 514 595
Chern isomorphism      343 485
Children of a tree vertex      601
Chirallty element      179 562
Chlral fermions      562
Christoffel symbol      256 382 409
Christoffel symbol, isotropic      410
Classical dimension      481 488
Classical symbol      301
Clifford algebra      172 214 333 504 559
Clifford bundle      370 504
Clifford connection      385 512
Clifford group      190
Clifford module      371
Clifford module, irreducible      372

Closed operator      393
Closed range      141 146
Coadjoint orbit      114 421
Coalgebra      35 598
Coassociativtty      35
Coboundary      223 599
Cocomimitativity      35
Cocompact subgroup      550
Cocycle      236 525
Codifferential      424
Cofunctor      9 53
Cofunctor, full      10
Cofunctor, halfexact      103 109
Cograph      628
Cohomology of a bicomplex      433
Coincidence limit of a kernel      277
Collapsing map      11 17
Column vectors      80
Comer of a C*-algebra      165
Commutant      483 542
Commutation relation      198 221 249 383 526
Commutative superalgebra      356
Commutator      173 269 625
Commutator Ideal      344
Compact group      44 54 623
Compact Hausdorff space      4
Compact Lie group      416 420
Compact operator      85 310 373
Compact pair      11 21 103
Compact perturbation      141 150 155
Compact resolvent      273
Compact space      4 15
Compactification      13 15
Compactification, one-point      4 11
Compactification, Stone — Cech      13 15
Complemented submodule      70 86
Complete symbol      507
Complex projecttve space      75
Complex structure      184 226 238 240 327 570 573
Complexffication      61 173
Conditional trace      329
Conditional-expectation      536
Cone algebra      23 26
Cone of a morphism      25
Conjugate space      160 380
Connected bialgebra      618
Connecting homomorphism      105 126 130 150 436
Connection      56 253 335
Connection 1-form      262 632 635
Connection Lapladan      259 262 394
Connection, affine      254
Connection, Clifford      385 512
Connection, dual      426
Connection, Hermittan      338 383
Connection, Levt-Civita      254 337 382
Connection, spin      383
Connection, tensor product      336 385
Connection, torsion-free      254 426
Connection, universal      336
Connes bicompkx      434 637
Connes boundary map      431 452 498
Connes — Moscavid algebra      612
Connes — Moscovid weight      609 617
Connes' distance formula      390 505
Connes’ character formula      479 493 498
Continued fraction expansion      531 556
Continuous field of C*-algebras      69 167
Continuous field of elementary C*-algebras      373
Continuous field of Hilbert spaces      67 373
Continuous field, locally trivial      68
Continuous linear functional      29
Contractible C*-algebra      23
Contractible chain complex      344 433
Contractible space      17 53 143 156
Contracting homotopy      344 361 433
Contraction      172 253 371
Contragredlent operator      228
Convolution      38 523 630
Coordinate functions      494
Coproduct      35 599 604 612 613
Correlation of operators      450
Corrugation operator      381 403 413 487 505 581
Cotangent bundle      264 305 349
Counit      35 599 602
Counterterm map      628
Counting function      272 316
Covariant representation      524 527 632
Cramer's rule      205 206 260
Creation operator      187 427
Cross-norm      24 32
Crossed product      167 524 529 550 631
Crossed product, iterated      534 556
Current      242
Current group      235
Curvature      338
Curvature, Riemannian      255 339
Curvature, scalar      256 270 395 414 511
Cutoff      307 471
CW-complex      23 108 137 343
Cycle over an algebra      326 350
Cyclic category      439 637
Cyclic cocycle      350 352 498 540
Cyclic cohomology      344 432
Cyclic cohomology of Hopf algebras      637
Cyclic cohomology, analytic      446
Cyclic cohomology, asymptotic      446
Cyclic cohomology, entire      449
Cyclic cohomology, periodic      444
Cyclic pennuter      350 365 430 438 638
Cyclic skewsymmetrizer      365 430
Cyclic vector      31 216 541
de Rham boundary      355 364 365 442
De Rham cohomology      325 340 426 490
de Rham complex      325 355 423 442
De Rham current      355 362
de Rham current, closed      499
de Rham homology      442 444
Deformation of C*-algebras      69 111
Deformation retract      89 91 137
Degeneracy operators      430
Dense ideal      27
density      257
Dequantization      114 123
Derivation      211 320 325 382 446 543
Derivation, inner      320
Derivation, symmetric      540
Determinant      131 217 580
Diagonal submanifold      357
Diagram      627
Dictionary of spaces and algebras      15
Diffeomorphism group      12 240 631
Differential      322
Differential form      325 371
Differential operator      136 298
Differential operator, elliptic      427 504
Differential operator, first-order      502
Dimension spectrum      480
Dirac adjoint      583
Dirac equation      559 573
Dirac geometry      487 545 548
Dirac K-cycle      479
Dirac operator      261 387 406 411 487 506 545 559
Dirac operator, equivariant      417
Dirac operator, generalized      387 512
Dirac operator, spectrum      419
Dirac sptnors      397
dispersion relation      589
Distance      272 390 391 492
Distance geodesic      388
distribution      9 275 298 360

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