Azcarraga J., Izquierdo J. — Lie groups, Lie algebras, cohomology and some applications in physics :: Электронная библиотека попечительского совета мехмата МГУ

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Azcarraga J., Izquierdo J. — Lie groups, Lie algebras, cohomology and some applications in physics

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Название: Lie groups, Lie algebras, cohomology and some applications in physics

Авторы: Azcarraga J., Izquierdo J.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 474

Добавлена в каталог: 09.03.2014

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Предметный указатель

$DiffS^{1}$       332 345
$H^{0}_{\rho}(\mathscr{G}, V)$       233
$H^{0}_{\sigma}(G, A)$       219
$H^{1}_{\rho}(\mathscr{G}, V)$       234
$H^{1}_{\sigma}(G, A)$       220
$H^{2}_{\sigma}(G, A)$       220
$\hat{A}$ -roof genus      147 391
$\kappa$ -symmetry      312 314
$\mathscr{F}(M)$ -linearity in $\mathscr{G}(M)$       338
$\mathscr{F}(M)$ -valued algebra cohomology      262
$\mathscr{F}(M)$ -valued cochains on G      226
$\mathscr{G}$ -valued differential forms      59
$\mathscr{G}(M)$       337
$\mathscr{G}(M)$ , Kac — Moody      334 340—345 349 397
$\mathscr{G}(M)$ , Virasoro      332 345—351 354
$\mathscr{G}(M)$ , Weyl — Heisenberg      343
$\phi$ -invariant vector field      9
$\phi$ -related tensor fields      35
$\phi$ -related vector fields      8 37
1-jet prolongation      282 291
1-jet section      282
Abelian U(1) or axial anomaly      366—372
Actions of a Lie group      4
AdG-invariant polynomials      104 105 385
Adjoint action      4 27
Adjoint representation of a group AdG      27 65
Adjoint representation of an algebra $ad\mathscr{G}$       66
Algebra cocycles      232
Algebra cocycles, simple cases      233
Algebra of equal-time charges      340
Algebra of vector fields      7
Anomalies, abelian or U(1)      366—372
Anomalies, cancellation      385—387
Anomalies, chiral or non-abelian      366 379—417
Anomalies, consistency (Wess — Zumino) condition      366 382 395
Anomalies, finite and infinitesimal versions      395
Anomalies, global (Witten's)      365
Anomalies, safe groups or algebras      365 385
Anomalous divergence      368—371
Anomalous Gauss law      396—397
Anomalous quantum theory      366
Anti-homomorphism      4 12 13
Anti-instanton solutions      127 130
Anti-self-dual gauge fields      49 127
Anti-unitary operators      159
Anticommuting variables      70
Antiderivation      35—36
Antisymmetric tensor field      32
Antisymmetric tensors, higher order      125
Associated, bundle      26
Associated, principal bundle      28
Associated, tensor bundle      26
Associated, vector bundle      25
Associativity breaking      187
Associator      279
Atiyah — Singer theorem      143
Atlas      2
Baker — Campbell — Hausdorff group      333 363
Banach space      332
Bargmann, Galilei two-cocycle      171
Bargmann, superselection rule      157
Betti numbers      43 45
Betti numbers of groups      78—80 248
Bi-invariant forms      63 80 248
Bi-invariant measure      58 60
Bi-invariant measure on GL(n, R)      66—67
Bi-invariant metric      64—65
Bianchi identity      92 94 98 127
Bott's periodicity      74
Boundary of a manifold      42
Boundary operator      8 46
BRST cohomology      249—253
BRST cohomology, formalism for gauge algebras      378
BRST cohomology, n-cochains      251
BRST cohomology, operator      250 308—309 407
BRST cohomology, transformations      378
Bundle      12
Bundle of Lie algebras      27 363
Bundle of Lie groups      27
Bundle of linear frames      26 30 84 96
Bundle of orthonormal frames      30 96
Bundle of Yang — Mills connections      361 363
Bundle, 1-jet      282
Bundle, associated      25—26 28
Bundle, base manifold      13
Bundle, coordinate      16
Bundle, cotangent      23
Bundle, diffeomorphisms      30
Bundle, equivalent      30
Bundle, examples      16—20
Bundle, homomorphism      28
Bundle, instanton      21 100 149
Bundle, local triviality      13—15
Bundle, morphism      29
Bundle, principal      13
Bundle, projection      13 22
Bundle, reduced      30 96
Bundle, structure group      13
Bundle, subbundle      30
Bundle, tangent      22
Bundle, tensor      23
Bundle, tensor product      23
Bundle, total manifold      13
Bundle, trivial      15—16 29
Bundle, vector      22
Bundle, Whitney sum      23
Bundles over contractible manifolds      20
Bundles over spheres      21
Canonical form on a Lie group      59
Canonical parallelism      60
Cartan calculus      31—43
Cartan decomposition      37
Cartan homotopy formula      110
Cartan homotopy operator      110 401
Cartan structural equation      92
Cartan — Killing tensor      63—65
Casimir invariants      80 249 385
Casimir operators      385
Casimir polynomials      248
Cech cohomology      21
Central charge      224 242 297
Central extension      162—163 168 189—192 221 238 295 301 341 347
Centre of a G-kernel      205
Chain rule      6
Characteristic class      104—120
Characteristic function      42
Characteristic module      292
Characteristic number      104
Characteristic polynomial      105
Characteristic vector field      165
Charge densities      319 338
Chern character form      114 391 400 408
Chern characters      114—115
Chern classes      104 111—112
Chern classes and infinite-dimensional Lie algebra cohomology      335
Chern classes and instantons      127
Chern classes, splitting principle for      115
Chern forms      112 385
Chern numbers      113
Chern — Simons form      109 116 391 418—420
Chern — Simons form, gauge transformation properties      118
Chern — Simons secondary class      109
Chern — Simons secondary class, generalization      110
Chern — Weil theorem      106 131
Chevalley — Eilenberg (p+2)-cocycles on $\sum$       314
Chevalley — Eilenberg cohomology      246—248 252 287 290 326 335 415
Chevalley — Eilenberg cohomology on $DiffS^{1}$       351
Chiral fermionic fields      366 379 380
Chiral or axial currents      368
Chiral superfields      73

Christoffel symbols      90 95
Classical anomalies      303
Classical compact groups      74
Clifford algebra      145
Coadjoint action      178
Coadjoint orbits      176 181 184
Coadjoint representation ad* of $\mathscr{G}$       66
Coadjoint representation Ad* of G      66 174
Coboundary operators, left action      216 227 231
Coboundary operators, right action      216 228 232 375
Coclosed form      53
Codifferential $\delta$       46—47 49—53
Codifferential $\delta$ as a divergence      50
Coexact form      53
Cohomological descent      303 308—309 394 398—416
Cohomological descent, ambiguity      405
Cohomological descent, cochains and coboundary operators      398—399
Cohomological descent, equations      403—408
Cohomological descent, non-triviality of the cocycles      415
Cohomology and classical mechanics      281 297—308
Cohomology of groups      215—229
Cohomology of Lie algebras      230—263
Cohomology on G(M), $\mathscr{G}(M)$       374—377
Cohomology on infinite-dimensional Lie algebras      335 348
Cohomology, Cech      21
Cohomology, Chevalley — Eilenberg      246—248 252 287 290 326 335 415
Cohomology, de Rham      43 80 107 248 287
Cohomology, equivariant      54 81
Cohomology, groups for semisimple algebras      242—243
Cohomology, groups of a compact group      254
Commutators      341
Complete Lorentz group L, extensions      275—279
Composite mapping theorem      7
Conformal, algebra      356
Conformal, anomaly      348 357 366
Conformal, group      354
Conformal, group in two dimensions      356
Conformal, invariance and self-duality      121
Conformal, Killing vector      355
Connected sum      136
Connection      84—95
Connection on $S^{n}$       100
Connection on a Lie group      100
Connection, affine space      90
Connection, flat      91 93
Connection, form      88
Connection, interpolating family of      107
Connection, linear      95
Connection, local representatives      89—90
Connection, reducible      96
Consistent anomalous theories      416—417
Consistent anomaly      381 395
Construction of the extensions      272
contact forms      283
Contractible manifold      44
Contractions and group cohomology      192—197
Contravariant vector field      31
Convex set      332
Coordinate bundle      16
Coset spaces      17
Cotangent bundle      23
Coulomb gauge      361
Covariant conservation      380
Covariant derivatives      95 361
Covariant derivatives on superspace      73
Covariant differentiation      40
Covariant divergence      385
Covariant vector field      23 31
Covector field      23
Critical trajectories      285
Cross section, global      15
Cross section, local      13
Cross section, natural      14—15
Crossed homomorphism      222
Current algebra      338 345
Curvature two-form      91 101 324
d, $\delta$ and $\Delta$ : relations between them      51
De Rham cohomology      43 80 107 248 287
de Rham cohomology on spheres      44
de Rham cohomology, coboundaries      43
de Rham cohomology, cocycles      43
de Rham cohomology, groups      43
de Rham cohomology, ring      45
de Rham complex      137 139
Derived series      243
Descending central series      243
Descent equations      403—408
Determinant bundle      394
Differentiable exponents      161
Differentiable manifold      2
Differentiable mapping      8
Differential forms      23—24 31—43
Differential mapping      6
Differential structure      2
Differential structure, exotic smooth structures      131
Dilatations      356
Dirac brackets      319
Dirac string      123
Dirac's quantization condition      125
Direct product of groups      192 223
Division algebras      21
Double cohomology sequences      308—309 322 403—404
Dual tensor      98
Dynamical groups      173
Effective action      4
Eilenberg — MacLane theorem      272
Electric current      121
Elliptic complex      141
Elliptic complex, classical      144
Elliptic complex, two-term      142
Elliptic operator      140 369 381
Embedding      29 30
Equivariant form      102—103
Equivariant function (G-function)      28
Euclidean group $E_{2}$       254
Euclidean space      387
Euler class      104 135
Euler form      135
Euler — Poincare characteristic      44—45 78 136 138
Euler — Poincare characteristic for the spheres      44
Euler — Poincare characteristic of a Lie group      80
Evolution space      282 290
Evolution space, enlarged      293
Exact sequences      199—201
Exotic smooth structures      131
Exponential groups      254
Extended Galilei algebra      170 182 286
Extended Galilei groups      158 169 206 300
extended objects      125
Extended objects, supersymmetric      313 315—324
Extendible G-kernel      204 268
Extensions of G by an abelian group A      221—223
Exterior covariant derivative      91 324
Exterior derivative d      35
Exterior functional derivative      316 352
Exterior product $\wedge$       32
External automorphisms      203
f-orbit      4
Factor system      199 209—211
Faddeev — Popov ghost fields      250 378
Faithful action      4
Fermionic functional      367
Fermionic functional, determinant      380 387—390
Fermionic functional, measure      367 380
Field strength F, electromagnetic      48
Field strength F, Yang — Mills      98
Forms      23—24 31—43
Forms, closed      43 139
Forms, coclosed      53 139
Forms, coexact      53

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