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| Gracia-Bondia J.M., Varilly J.C., Figueroa H. — Elements of Noncommutative Geometry |
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| Предметный указатель |
Distribution, operator-valued 583
Distribution, periodic 275
Divergence formula 392
Divergence of a vector field 259
Dixmier trace 251 288 464 465 470 549
Dixmier trace class 398
Dixmier — Douady class 373
Dlxmier ideal 286 316 317
Domain of an operator 393
Dual A-module 57 73 75 482
Dual Banach space 315
Dual of a Hopf algebra 598 623
Duhamel equation 455
Dunford integral 28 134 281
Dyson expansion 571
Dyson expansion, quantum 586
e-Theory 110 130
Effective action 592
Eigenschaften algebra 520
Eigenspinor 396 414
Eilenberg — MacLane space 75
Einstein — Hilbert action 270 492 507 512
Eisenstein series 335 549
Elementary C* -algebra 167 373
Elementary particles 519
Elliptic curve 398 549
Elliptic operator 263 276 327 400
Elliptic operator, differential 392 425 488
Elliptic operator, pseudodifferential 158 293 303
Endomorphism algebra 83
Entire cochain 449 454
Entire cyclic cohomology 449
Enveloping C*-algebra 524
Epstem — Glaser renormalization 592 630
Equivalence bimodule 162 375 377
Equivalence of categories 11
Equivalent projectors 91
Essential extension 84
Essential ideal 13—15 84
Essentially selfadjolnt operator 393
Euler angles 417
Euler characteristic 361 428
Euler vector field 264 266 361
Evaluation map 5 10 43 45 63
Exact couple 441
Exact sequence of vector bundles 51
Exact sequence, augmentation 22
Exact sequence, split 25 51 58
Excision 103 446
Extended orthogonal group 236
Extension of C*-algebras 22
Extension of scalars 60
Exterior algebra 172 184
Exterior bundle 370
External lines 627
Faithful state 30 529 535
Fermion field 249
Feynman graph 627
Feynman rules 578
Feynman slash notation 559
Filtration 618
Finite-rank operator 142 284 471 496
Finite-rank projector 143
Finitely generated module 79
Finitely generated projectlve module 59 74 101 164 482 489 500 554 556
First order condition 489
First-order differential calculus 321
Flag manifold 420
Fock representation 187 215
Fock space 186 215 399
Fock space, bosonic 201
Fock space, polarized 186
Fock state 215
Forest 628
Formal quantum field theory 582
Formally selfadjoint operator 391
Fourier kernel 114 118
Fourier series 526 528
Fourier transform 6 271 309 331
Frame 90
Frame bundle 631
Frechet algebra 9 357 469 483
Frechet space 12 467 535
Fredholm index 142 397
Fredholm operator 142 226 446 480
Fredholmmodule 326 400 444 446 462 493
Free Hamiltonian 576
Free module 79
Full corner 165
Fun C* -module 65
Functional calculus 28 29 274 450
functor 9 95
Functor, continuous 98
Functor, contravariant 9
Functor, exact 58
Functor, faithful 58
Functor, full 58
Functor, halfexact 98 105
Functor, homotopy-invariant 98 105
Functor, K-theory 98 128
Functor, normalized 98
Functor, stable 98
Fundamental 1-form 254 337
Fundamental class 499
Gamma matrices 545 562
Gauge fixing 385 409 411
Gauge potential 386
Gaussian 208 217
Gaussian elimination 135
Gelfand spectrum 5
Gelfand topology 5 9
Gelfand transformation 5
Gelfand — Fuchs cohomology 640
Generalized Dirac operator 420
Generalized limit 288 290 464 473 474
Geometric quantization 421
GLS symbol 117 275
GNS construction 30 167 214 541
Good locally convex algebra 135 469
Graded bialgebra 38 620
Graded differential algebra 322 348
Graded differential algebra, universal 323
Graded module 188
Graded tensor product 210
Gradient 252 505
Grading operator 188 212 330 372 424 488
Graph 627
Grassmann variables 203
Grassmannian 53
Grossman — Larson Hopf algebra 614 618 626
Grossmann — Royer reflection operators 115
Grothendieck group 92
Ground state 122
Group action 138 523 631
Group action, ergodic 537
Group algebra 40
Group C* -algebra 525
Group C* -algebra, twisted 526 533
Group-like element 40 46 624 636
Haagerup tensor product 33 46 166
Haar functional 43 46
Haar measure 43 418
Halfexact cofunctor 103 109
Halfexact functor 98 105
Hamiltonian density 582
Harmonic form 425 428
harmonic oscillator 122
Heat kernel 280
Heat kernel, expansion 283
Heaviside function 275 566
| Heisenberg equation 198
Heisenberg group 67
Hermitian metric 65
Hermitian pairing 65 370 371
Hermitlan connection 338 383
Hexagon 126 343
Hilbert module 65
Hilbert transform 330
Hilbert — Schmidt operator 217 225 240 248 311 328 495 573
Hochschild boundary 348
Hochschild coboundary 349 430 599
Hochschild coboundary, truncated 430
Hochschild cocycie 349 470 476
Hochschild cohomology 349 430 438
Hochschild cohomology, continuous 356
Hochschild cycle 484 489 493 514 515 547
Hochschild homotogy 345 447 513
Hodge star operator 423
Hodge — de Rham Lapladan 261 425
Hodge — Dirac operator 426
Holder inequality 289 312 316 453 458 465 500
Holomoiphic functional calculus 28 134
Holomoiphic functional calculus, stability under 134
Homeomorphism 10 15
Homogeneous distribution 271 306
Homogeneous function 265 266 306
Homology module 105 344
Homology theory 105
Homotopic morphisms 16
Homotopic projectors 91
Homotopy class 17 20 111
Homotopy equivalence 16 17 53 137
Homotopy group 77 121
Homotopy invariance 341
Hopf algebra 34 39 601
Hopf C*-algebra 46
Hopf module algebra 47
Horn's inequaUty 289
Hubert algebra 179
Hubert space 30 65
Hubert space, virtual 422
Hyperbolic automorphism 533
Hyperplane bundle 78 408
Hypertrace 465 498
Ideallzer 14
Idempotent 18 81 87 93 137 343
Implementation problem 224 573 594
Implementor 191 562
INDEX 142 145 149 227 397
Index formula 243
Index map 130 144 154 234
Index of an odd operator 397
Index pairing 446 480 485 547
Inductive limit 56 117 358
Infinitesimal element 141
Infinitesimal operator 284
Infinitesimal spin representation 195 221 383
Inner automorphism 215
integral 326 333
Integral of a function 297
Interaction Hamiltonian 576
Interaction representation 571
Internal lines 627
Interpolation inequality 317 464
Invartance under Hopf action 636
Invertible element 18 93 134 135 147 482
Involution 27 175 338 483
Irrational rotation algebra 523
Irreducible complexity 126
Irreducible representation 31 184 215 418
Isotropic subspace 185
Jacobi identity 211 223 484
JLO cocycle 451
Joint spectrum 494
Jordan — Paull function 567
K-cycle 400
K-cycle, unbounded 401
K-homology 400 446 485
K-orientation 379
K-theory functor 98 128
K-theoryof tori 133 556
Kaehler differentials 322
Kaplansky’s formula 88 122 147 482
Kernel of a pseudodifferential operator 271 277 299
Ketbra 71
Killing form 420
KR-homology 400 483
Kronecker flow 523 553
Kronecker foliation algebra 553
Laplace expansion 219
Laplace transform 273
Laplace — Beltraml operator 259 260 425
Lapladan 259 272 291
Lapladan, generalized 263
Lapladan, scalar 398 511
Lapladan, spinor 398 511
Leaf of a rooted tree 601
Lebesgue measure class 494
Leibniz rule 47 253 320 321 335 382 383 502 632
Length of a curve 388
Length of a tree vertex 601
Levi-Civita connection 254 337 382 409 427
Lichnerowlcz formula 395 398 413 419 511
Lie algebra 38 139 182
Lie algebra cohomology 223
Lie algebra, restricted orthogonal 221
Lie derivative 253
Lie group 121 138 420
Lie superalgebra 211
Line bundle 20 75
Line bundle, canonical 421
Line bundle, Hopf 121
Line bundle, tautological 78 121 408
Liouville measure 113
Lipschltz function 389
Local frame 50 55 631
Local orthonotmal basis of 1-forms 382 406 423
Local section 50
Local uniform closure 67
Locality of Hochscbild homology 357
Locally compact space 4
Locally convex topology 134 356 469
Logarithmic element 18 128 183
Long Exact Sequence 19 104 378 436
Lorentz product 558
Lorentz transformations 558
Macaev ideal 316 317
Majorana field 244
Majorana spinor 407
Manifold 251 487
Mapping cone 23
Mapping cone, unreduced 26
Mapping cylinder 23 25
Matrix algebra 32 93 503
Matrix-valued 501
Mavimal C* cross-norm 33 113
Maximal ideal 7
Mayer — Vletoris sequence 127
Measurable operator 288 293 489 493 545
Mellln transform 283
Metaplectk representation 116 182
Metaplectlc structure 382
Metrizable space 15
Minimal coupling 263
Minkowski space 558
mod-2 reduction 378
Modular pair 46 636 638
Module morphism 61
Moebius transformation 417
Moment asymptotic expansion 118 275
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