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

Moment of a distribution      118 284
Morita equivalence      162 164 166 177 375 482 491 502 504 549 553
Morita invariance      103 165 556
Morphism      10 15
Morphism of C* -algebras      10 29 112 136
Morphism of C*-modules      70
Morphism of Hopf algebras      39
Morphism, bialgebra      40
Morphism, bundle      52
Morphism, module      61
Morphism, restriction      12 63
Morphism, unital      29
Morphism, Woronowicz      15 46
Moyal algebra      117 539
Moyal asymptotic morphism      120 122
Moyal product      116 539 593
Moyal pseudodifferentlal calculus      115
Moyal quantization      67 113 120 201
Moyal quantizer      113 115
Moyal quantum mechanics      111 123
Multiplication map      34 46 124 320
Multiplication operator      14 328 495
Multiplicity function      495
Multiplier algebra      14 15 84 117
Musical isomorphisms      252
n-simplex      438
n-skeleton      109
Natural growth operator      609
Natural transformation      10 105
Neutrino field      561
Neutrino paradigm      562
Noncommutadve pullback bundle      62
Noncommutative integral      285 297 398 399 493 546 548
Noncommutative residue      267
Noncommutative space      8
Noncommutative spin geometry      485 492 545
Noncommutative torus      102 529 535
Noncommutative Yang — Mills theories      593
Nonunital C*-algebra      14 97 128
Normal coordinates      257 361
Normally ordered product      230
Nuclear C*-algebra      33
Number operator      122 197 509
Number operator, quantized      242
One-point compactification      4 11
Operator ideal      311 313
Operator module      166
Opposite algebra      61 175 353 481 488 542
Ordered group      96
Orientable manifold      371 499
Orientation class      422
Orientation cycle      488 493
Oriented      179 188
Orthogonal complex structure      184
Orthogonal group      180
Orthogonal projector      54
Orthononnal basis      54
Out-vacuum vector      228 233 242
Pairing      65 159 423 448 471 500 551 553 622
Paracompact space      50
Parametrix      303 327 393
Parity      210
Parseval — Plancherel formula      418
Partial trace      514
Partition of unity      20 50
Path component      128 137
Pauli matrices      76 333 411 560 595
PBW basis for U(g)      37 621
Penrose tiling      96
Periodic cyclic cohomology      444 540
Periodicity operator      353 440 541
Pfaffian      204 217
Phase of the scattering matrix      585 586
Phase operator      446 545
Phase space      113
Pimsner — Voiculescu embedding      531
Pimsner — Volculescu hexagon      556
Planck's constant      111
Plcard group      74 376
Poincare duality      361 426 485 490 547
Poincare group      558
Point at infinity      4
Pointed space      11 17 23 101
Poisson bracket      302
Polar decomposition      143 233 310 314
Polarization      185 421
Polarization, restricted      226
Polarized Fock space      186
Pontryagin duality      46 599
Positive element of a C*-algebra      29
Positive linear functional      15 29 290
Positive square root      29 73
Pre-C*-algebra      134 469 482 489 529
Pre-C*-module      65 159
Pre-Fredholm module      327 400
Primitive element      38 610 615 619
Primitive graph      628
Primitive of a distribution      275
Principal bundle      234 264 631
Principal homogeneous space      377
Principal symbol      301 393 422 502 506
Principal value distribution      307
Product of spin geometries      486
Projecrive module      80 336 353
Projective resolution      353 360
Projectlve tensor product      33 357
Projector      54 71 76 86 112 185 529
Projector of rank one      373
Projector, minimal      503
Projector, Powers — Rieffel      529 547
Propagator      564
Propagator, advanced      566
Propagator, Dyson      567
Propagator, Feynman      566 579
Propagator, quantum      586
Propagator, retarded      566 575
Propagator, unitary      571
Proper ideal      27
Proper map      10 15
Protective representation      114 115 194 236
Pseudo-Riemannian manifold      252
Pseudodlfferential operator      266 298 327 331
Pseudodlfferential operator on a manifold      304
Pseudodlfferential operator, classical      266
Pseudodlfferential operator, elliptic      506
Pseudodlfferential operator, order of      299
Pseudodlfferential operator, properly supported      300
Pseudoinverse      146 149
Pullback      21 64
Pullback bundle      52
Puppe sequence      25
Puppe sequence of C*-algebras      104
Puppe sequence of spaces      108
Pure state      8 30 391
Q-algebra      135
Quadratic form      173 503
Quadratic form, positive definite      179 510
Quantization      113 250 422 538
Quantization map      173 396
Quantum dimension      594
Quantum electrodynamics      573
Quantum field theory      522
Quantum Hall effect      521
Quantum plane      36
Quite irrational matrix      537
Quotient space      11 167
Range of a projector      86 88
Rank of a CW-complex      109
Rank of a vector bundle      50
Rank-one projector      122

Rapidly decreasing sequence      528 535
Real structure      483
Realisation      238
Reduced -ring      101
Reduced suspension      109
Reflection      180'
Regular operator      146 151
Regularization of distributions      306 589
Renormalization      592 627
Representation of $SL(2,\mathbb{C})$       560
Representation of a C*-algebra      31 159 167
Representation, irreducible      31 184 191 215
Representation, type of      189 407
Representative function      34 42 623
Reproducing kernel      113
Reproducing property      114
Residue calculus      566
Resolvent equation      273
Restricted orthogonal group      225 236
Restricted orthogonal lie algebra      221
Restriction of scalars      60
Ricci tensor      256
Riemann curvature tensor      384
Riemann sphere      75 292 515
Riemann zeta function      250 283
Riemannian curvature      255 256 339
Riemannian density      258 389 399 507
Riemannian manifold      252
Riemannian metric      76 2 388 492 304
Riesz operator      332
Riesz theorem      160 380
Rooted tree      601 613
Rotation      194 559
Rotation group      180
Row vectors      66 80
Rules      578
Runge — Kutta method      617
Scalar curvature      256 270 283 395 414 511
Scalar Laplacian      398 511
Scalar product      66 179 184 186 423 500
Scattering matrix, classical      245 572
Scattering matrix, quantum      245 247 576 582
Schatten p-class      285 311 317 328 462 482
Schur's lemma      187 193
Schwartz space      115 135 535 549
Schwarz inequality      30 69 84 119 389
Schwarz inequality, generalized      537
Schwinger function      567
Schwinger term      222 223 298 351
Second-quantized operators      196
Section      50
Section of a continuous field      67 111 373
Section, along a map      62
Section, of a vector bundle      56
Section, smooth      60 339
Selfadjoint element      6 28
Selfadjoint operator      273
Separating duality      623
Separating vector      31 541
Series reversion      278 634
Sesquilinear form      65
Shift operator      525
Short exact sequence      19 131 235
Short exact sequence of C*-algebras      21 98 105
Short exact sequence of groups      181
Short exact sequence of modules      50
Short exact sequence of sheaves      375
Shuffle permutation      190 205 424
Shuffle product      348 356
Signature of a quadratic form      174
Signature operator      427
Similarity of idempotents      89 91
Simple cut      602
Simplicial category      438
Singular value      217 248 284 311 464
Skewadjoint operator      195 541
Skewgroup      43
Skewsymmetric matrix      204
Skewsymmetrizatlon      347 355 363 490 499
Smash product      23 47 622 632
Smooth domain      276 468
Smooth element      138
Smooth rapidly decreasing functions      135
Smoothing operator      266 299
Sobolev space      300 306 466
Sobolev's lemma      300
Spectral asymmetry      281
Spectral density      274
Spectral function      272
Spectral measure      495
Spectral projector      112 471
Spectral radius      6 7 28 111
Spectral sequence      441
Spectral triple      401 446 487
Spectral triple, $\theta$ -summable      450
Spectral triple, p+-summable      450 457 465 482
Spectral triple, real      481
Spectral triple, regular      466 482 489
Spectral triple, tame      465
Spectrum      5 28 134 136 167 310
Spectrum, absolutely continuous      495
Spherical harmonics      415
Spin connection      383 411
Spin connection, twisted      427
Spin curvature      384
Spin geometry      485 488
Spin geometry irreducible      491
Spin geometry, $\theta$ -dimenslonal      486
Spin group      181
Spin manifold      381 421
Spin representation      192 235 585
Spin structure      381 408 421 487 492 505
Spin group      181
Spin manifold      378
Spin structure      378 504 512
Spinor      186 409
Spinor bundle      379 500
Spinor harmonics      408 415
Spinor Laplacian      394 398 411 413 419 511
Spinor module      409 487
Spinor space      389 487
Split      22 25 80 108
Splnorial dock      177 *
Stable C*-algebra      85
Stable homptopy      121
Stable range      121
Stably equivalent C*-algebras      85 165
Stably equivalent vector bundles      102
Stably quaslisomorphlc C*-modules      149
Standard model      519
State      30 215 391
Stereographic projection      75
Stiefel — Whitney class      381 421
Stone — Cech compactification      13 15
Stratonovtch — Weyl quantizer      114
Subbundle      51
Subdlagram      627
Subgraph      628
Subpfafflan      205 208
Superalgebra      210
Supercommutator      173 175 211 328
Superficial degree of divergence      627
Supermechanics      62
SuperrepresentaUon      188 211
Superspace      188 210
Supertrace      202 212 330
Suspension      24 108 109
Suspension, unreduced      26
Symbol      298
Symbol calculus      269 301

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