Mackenzie K.C.H. — General Theory of Lie Groupoids and Lie Algebroids :: Электронная библиотека попечительского совета мехмата МГУ

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Mackenzie K.C.H. — General Theory of Lie Groupoids and Lie Algebroids

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Название: General Theory of Lie Groupoids and Lie Algebroids

Автор: Mackenzie K.C.H.

Аннотация:

Groupoids possess пишу of the features which give groups their power and importance, but apply in situations which lack the symmetry which is characteristic of group theory and its applications. Though only developed since the mid 20th century, the modern concept of Lie groupoid is as much entitled as is the familiar concept of Lie group to be regarded as the rigorous formulation of the 19th century notion which went under the then vague term 'continuous group of local transformations'; a case could be made that the modern concept of Lie group has been a transitional stage in the evolution of the notion of Lie groupoid.

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Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2005

Количество страниц: 501

Добавлена в каталог: 07.11.2009

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Предметный указатель

$\alpha$ fibre      5
$\alpha$ -connected      6 49
$\alpha$ -homotopy      216
$\alpha$ -path      216
$\beta$ -fibre      5
$\Gamma$ -lift      228 229 234
$\mathcal{LA}$ groupoid      xviii 443 471
$\mathcal{VB}$ -groupoid      415
$\mathcal{VB}$ -groupoid dual      418
$\mathcal{VB}$ -groupoid tangent      415
$\mathcal{VB}$ -groupoid, tangent prolongation of      431
$\Omega$ deformable      40 52
$\Omega$ invariant      13
$\Sigma$ bundle      52 147
$\Theta$ stable      57 60
Action of equivalence relation linear      55
Action of Lie algebroid complete      406
Action of Lie algebroid generalized      172
Action of Lie algebroid infinitesimal      149
Action of Lie groupoid      34
Action of Lie groupoid by Lie group isomorphisms      47
Action of Lie groupoid linear      43
Action of Lie groupoid on Lie groupoid      77 84
Action of Lie groupoid right      42
Action of Lie groupoid trivial      35
Action of Lie groupoid, inner automorphism      36
Action Poisson      467
Action symplectic      471
Action, dressing transformation      413
Adjoint bundle of Lie algebroid      106 249
Adjoint bundle of Lie groupoid      130
Adjoint bundle of principal bundle      93
Adjoint LAB      see "adjoint bundle"
Adjoint representation of Lie algebroid      108
Adjoint representation of Lie groupoid      131
Anchor of Lie algebroid      100 123
Anchor of Lie groupoid      12
Anchor Poisson      383
Anchor-preserving map      265
Annuls      59 73 167
Antimorphism of Lie algebroids      453
AntiPoisson map      385
arrow      4
Arrow missing      350
Associated fibre bundle      20
Atiyah sequence      97
Atiyah — Lie algebroid      97
Baer sum      270 309
Base      4 100
Base double      340
Batalin Vilkovisky algebra      406
Bianchi identity      190 279
Bianchi identity abstract      265
Bisection      22 50
Bisection local      25
Bracket derivation outer      271
Cech class discrete      314 329
Chern class, first      312
Chern — Weil construction      286 309
Cohomological obstruction      328
Coisotropic submanifold      398
Comorphism of Lie algebroids      165 177
Compatibility condition      101
Complex structure      46
Congruence      68 84
Congruence uniform      76
Connection adjoint      190 195 249
Connection back      210
Connection contravariant      388 406
Connection form local      207
Connection G equivariant      201
Connection G invariant      201
Connection Gauss — Manin      309
Connection in Lie algebroid      186
Connection in Lie algebroid standard flat      188
Connection in Lie groupoid infinitesimal      186
Connection Koszul      see "Koszul connection"
Connection Lie      189
Connection local flat      206 318
Connection metric      188
Connection produced      189
Connection reform      186
Connection Riemannian      188
Conormal bundle      397
Contraction operator      306
Core element      111
Core of -groupoid      416
Core of double vector bundle      316
Core section      see "section core"
Cotangent double      471
Cotangent philosophy      381
Coupling of Lie algebroids      258 272 309
Coupling of Lie algebroids induced      278
Covariant derivative      191 275
Covariant differential operator      146
Crossed module      309 332
Curvature form, local      207
Curvature of anchor-preserving map      265
Curvature of Koszul connection      185
Curvature of Lie algebroid connection      187
Curvature of principal bundle connection      195
Curvature reduction      244
Cо star      49
Darboux derivative      182
Derivation      103
Derivation bracket      141
Derivation metric      141
Derivative endomorphism      103
Derivative representation      153 172
Descent      57 83 168
distribution      103
Double vector bundle      340
Double vector bundle triVial      345
Double vector bundle, core      346
Double vector bundle, dual cotangent      357
Double vector bundle, dual horizontal      350
Double vector bundle, dual prolongation      355
Double vector bundle, dual vertical      349
Double vector bundle, morphism      344
Double vector bundle, tangent      111
Double vector bundle, translation maps      316
Duality of double vector bundles      349
Duality of Poisson groupoids      444 445
Equally good      218
Equivariant      107
Equivariant under groupoid action      34
Euler class      312
Exponential map      133
Extenseurs reguliers      83 84
Extension flat      266
Extension geometric      290
Extension of Lie algebroids      109 266
Extension of Lie algebroids, equivalence      277
Extension of Lie groupoids      47
Extension operator      266 282
Extension operator equivalent      266
Extension pullback      270
Extension pushout      268
Extension restriction semi-direct      290
Extension RSD      290
Extension semi-direct      286
Fibration of Lie algebroids      166 176
Fibration of Lie algebroids, split      171
Fibration of Lie algebroids, uniform      170 176
Fibration of Lie groupoids      66 82
Fibration of Lie groupoids, split      79
Fibration of Lie groupoids, uniform      76 82
Fibration of set groupoids      83
Field of Lie algebra brackets      46 104
Flip of double vector bundle      341

Flow neighbourhood      133
Flow saturated local      97
Foliation      51
Foliation Stefan — Sussman      51
Foliation, characteristic of Lie algebroid      100
Form basic      196
Form equivariant      196
Form horizontal      196
Form linear      464
Form Liouville      386
Form multiplicative      464
Form pseudotensorial      196
Form right invariant      412
Form star      161
Form tensorial      196
Function multiplicative      373
G-simple cover      219
Gauge group bundle      11
Gauge transformation      25
Gerstenhaber algebra      304
Graded Jacobi identity      305
Graded Leibniz identity      305
Groupoid      4
Groupoid abelian      52
Groupoid action      7 37
Groupoid action right      42
Groupoid adjoint      332
Groupoid algebraic theory      18
Groupoid connected      50
Groupoid cotangent      419
Groupoid covering      51
Groupoid differentiable      19 474
Groupoid fundamental      8 19 51
Groupoid gauge      9 50
Groupoid Lie      5
Groupoid locally trivial      15
Groupoid monodromy      214 216
Groupoid monodromy (of a foliation)      473
Groupoid of inner automorphisms      315
Groupoid pair      7
Groupoid Poisson      420
Groupoid Poisson, pair      428
Groupoid prolongation      50
Groupoid quotient      73
Groupoid smooth      49
Groupoid symplectic      429
Groupoid topological      48
Groupoid topological principal      50
Groupoid totally disconnected      50
Groupoid totally intransitive      32
Groupoid transformation      51 see action"
Groupoid transitive      14
Groupoid trivial      7
Groupoid, base      6
Groupoid, coarse      49
Groupoid, etale      51
Groupoid, frame      8
Groupoid, frame complex      16
Groupoid, frame Hermitian      46
Groupoid, frame orthonormal      46
Groupoid, frame Riemannian      46
Groupoid, frame unitary      46
Groupoid, holonomy      473
Groupoid, interior Lie      315
Groupoid, jet prolongation      147
Groupoid, Morita equivalence of      84
Groupoid, set-      5
Groupoid, tangent prolongation      10
Groups importance of      32
Holonomy (of a foliation) groupoid      473
Holonomy bundle      232
Holonomy group      232
Holonomy group restricted      235
Holonomy morphism      226
Holonomy subgroupoid      232
Homology canonical      106
Homology Poisson      406
Horizontal bundle      311
Horizontal distribution      193
Ideal of inner derivations      105
Ideal of Lie algebra bundle      106
Ideal of Lie algebroid      250
Ideal reduction      250
Ideal system      167
Ideal system uniform      170
Identity      5
Image of Lie algebroid morphism      250
Inducteurs surmersifs      84
Inductor of Lie algebroids      176
Inductor of Lie groupoids      82
Inflation map      290
Inflation of Lie algebroid      290
Inner automorphism      17 24
Inner automorphism local      26
Inner group bundle      11
Insert operator      306
Integrability obstruction      326
Internalization map $\mathcal{VB}$ -groupoid      436
Internalization map groupoid      436
Internalization map, double vector bundle      355
Involution canonical      363
Isomorphism of Lie groupoids      12
Isotropy group      49 see
Isotropy subgroupoid      see "subgroupoid stabilizer"
Kernel      65
Kernel of Lie algebroid morphism      249
Kernel of Lie groupoid morphism      63
Kernel of Lie groupoid morphism, base-preserving      60
Kernel pair      51
Kernel system      58
Koszul connection in Lie algebroids      153 163
Koszul connection in vector bundle      109 185
Koszul connection in vector bundle associated      195
Koszul connection in vector bundle trivial      185
Koszul connection in vector bundle, Lie derivative      185
Koszul connection in vector bundle, standard flat      185
Koszul connection, curvature of      185
LAB      see "Lie algebra bundle"
Lagrangian submanifold      429
Lasso      218
Left-translation      5 22
Left-translation local      25
LGB      see "Lie group bundle"
Lie algebra bundle      104
Lie algebra bundle abelian      106
Lie algebra bundle adjoint      105
Lie algebra bundle centre      105
Lie algebra bundle derived      105
Lie algebra bundle nilpotent      106
Lie algebra bundle of a LGB      126
Lie algebra bundle of derivations      105
Lie algebra bundle quotient      106
Lie algebra bundle reductive      106
Lie algebra bundle semisimple      106
Lie algebroid      100
Lie algebroid conormal      398
Lie algebroid cotangent      383
Lie algebroid dual      423
Lie algebroid integrable      323
Lie algebroid locally trivial      205
Lie algebroid of Lie groupoid      123
Lie algebroid of Lie groupoid left      131
Lie algebroid of Lie groupoid symmetric      132
Lie algebroid quotient      168 251
Lie algebroid regular      100
Lie algebroid sequence      330
Lie algebroid transitive      100
Lie algebroid trivial      101
Lie algebroid, action      104 151
Lie algebroid, atlas      206

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