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

Symbol map      173 267
Symbol of spectral density      276
Symbol, Grossmann — Loupias — Stem      117 275
Symmetric algebra      38 620
Symmetric bilinear form      172 576
Symmetric bimodule      320
Symmetric gauge function      314
Symmetric norm      288 313 463
Symmetric operator      391
Symmetrically normed ideal      2 88 313 496
Symmetry      86 314 326
Symmetry via Hopf algebras      47
Symplectic cone      264
Symplectic form      115
Symplectic group      116 182
Symplectic homogeneous space      114
Symplectic manifold      264
Tangent algebra      324
Tannaka — Krein duality      46 617
Tempered distribution      298 300
Tensor algebra      37
Tensor product      85
Tensor product of asymptotic morphisms      113
Tensor product of C* -algebras      24
Tensor product of C*-bimodules      162
Tensor product of C*-modules      159 166
Tensor product of connections      255 336 385
Tensor product of Hilbert spaces      32 33
Tensor product of modules      57
Tensor product of vector bundles      100
Tensor product, $\mathbb{Z}_2$ -graded      189
Tensor product, algebraic      24 32 67 73
Tensor product, Haagerup      33 46
Tensor product, projective      33 357
Tensor product, spatial      33
Theorem, Arens — Royden      20
Theorem, Ativah — Jaenich      121 144 244
Theorem, Atkinson      141
Theorem, Banach — Alaoglu      5
Theorem, Bartle — Graves      112 120
Theorem, Bass      102
Theorem, Borel — Wefl      421
Theorem, Bott periodicity      121 125
Theorem, Calkin      313
Theorem, Chem Isomorphism      343 491
Theorem, classification      64
Theorem, Connes character      479 595
Theorem, Connes spin manifold      4921 513
Theorem, Connes trace      293 479 506
Theorem, Connes — Langmann      333 479
Theorem, divergence      259 392
Theorem, Ellott      96
Theorem, Euler      265
Theorem, family index      158
Theorem, Forster      75
Theorem, Fourier Integral      115
Theorem, Frobenius — Schur      191
Theorem, Furry      581
Theorem, Gelfand — Nabnark      7 29 31 288
Theorem, Hahn — Banach      8 31
Theorem, Hardy —Littlewood      296
Theorem, Hochscbild — Kostant — Rosenberg — Connes      355 363 442 485 499
Theorem, Hochschild — Kostant — Rosenberg      356
Theorem, Hurewlcz      75
Theorem, Ikehara — Wiener      296
Theorem, Kasder — Kalau — Walze      270 280 283 511
Theorem, Kasparov absorption      147
Theorem, Kato — Rosenblum      495
Theorem, Klee      12
Theorem, Kuiper      143 145
Theorem, Kuiper — Mingo      156
Theorem, Kuroda      495
Theorem, Lichnerowicz      395
Theorem, Lidskli      580
Theorem, Liouville      28
Theorem, local index      480 635
Theorem, Milnor      137 156
Theorem, Milnor — Moore      615 621 626
Theorem, Mishchenko — Fomenko      158
Theorem, Myers — Steenrod      388
Theorem, Nash embedding      337
Theorem, Nelson      216
Theorem, open mapping      112 142
Theorem, Panaite      626
Theorem, Peter — Weyl      45
Theorem, Plymen      375
Theorem, Poincare — Birkhoff — Witt      37
Theorem, Rellich      300 306
Theorem, Riesz      160 380
Theorem, Riesz — Markov      16
Theorem, Serre — Swan      59 91 101 360 370 500
Theorem, Shale — Stinespring      216 232
Theorem, Shilov      20
Theorem, Spectral      8 273
Theorem, stable range      102
Theorem, Stokes      259 326 364 499

Theorem, Stone — Weierstrass      7 16 45 138 324
Theorem, Tannaka — Krein      624
Theorem, Tikhonov      5 44
Theorem, Toeplitz — Schur      475
Theorem, Tomita      542
Theorem, Voiculescu      496
Theorem, von Neumann      483 542
Theorem, Weierstrass      146
Theorem, Weyl — von Neumann      495
Time-ordered product      572
Tomita conjugation      542
Topological $\mathcal{A}$ -module      357
Topological group      9
Topological K-theory      93
Topological stable rank      102
Topologically projective module      357
Torsion group      339
Torsion tensor      254 337
Torus      291 398 527
Total complex of a bicomplex      432
Total volume of a geometry      548
Trace      30 179 268 269 285 312 343 349 479 529 538 554 636
Tracedass operator      115 285 311 495
Tracial state      30 529 535 537
Transgression formula      455 459
Transition function      50 55 408
TRANSPOSE      200 598
Tree factorial      605
Triangle inequality      69 390
Trunk of a simple cut      602
Tsygan bicomplex      432
Twisting      376
Twisting of vector bundles      379
Type II factor      214
Type of the spin representation      407
U(1) gauge field      262
Ultraviolet divergences      593
Unbounded K-cyde      401
Unilateral shift      158
Unitalring      60 79 92 166
Unitary element      6 28 180 536
Unitary equivalence      86 216 224 233
Unitary equivalence of C*-modules      85 87 147
Unitary equivalence of geometries      486
Unitary group      54 156 185
Unitary operator      143 239
Unitary operator on a C*-module      85
Unitary operator, restricted      240
Unitization      14 15
Universal 1-form      321
Universal connection      336
Universal enveloping algebra      37 42 139 618 623
Unreduced cone      26
Unreduced suspension      108 109
Vacuum functional      237
Vacuum persistence amplitude      245 248 576 580
Vacuum polarization      585
Vacuum vector      186 208 215 226 228 242
Vector bundle      49
Vector bundle, dual      57
Vector bundle, equivalence      50 55
Vector bundle, Euclidean      370
Vector bundle, tautological      54 64
Vector bundle, trivial      50 52 101
Vector field      136 325
Vector field, horizontal      632 '
Vector field, vertical      632
Virasoro group      258
Virtual bundle      100 121
Virtual Hubert space      142
Virtual rank      101
Voiculescu's modulus      496
Volume element      258
Volume form      342 423 489 500 515 546
volume of a sphere      269
von Neumann algebra      129 483 542
von Neumann factor      214
Weak* topology      5 391
Weyl elements      534 535
Weyl neutrino equations      561
Weyl operators      115 539
Weyl spinors      397
Weyl's estimate      272 279 293
Whitney product formula      421
Whitney sum      52
Whitney sum of spin geometries      491 503
Wick rotation      568
Wick-ordered product      230
Wightman functions      567
Winding number      75
Wodzicki residue      251 267 282 479 492 506
Wodzicki residue, density      267 280
Zeta function      273 281
Zeta operator      274
Zeta residue      251 282
Zimmermann forest formula      608 628

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