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


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 501

Добавлена в каталог: 07.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Lie algebroid, direct product      156
Lie algebroid, direct sum over fixed base      110
Lie algebroid, pullback      157 269
Lie algebroid, semidirect product generalized      173
Lie algebroid, tangent prolongation      369
Lie algebroid, totally intransitive      100
Lie algebroid, transformation      151 see action"
Lie bialgebroid      447
Lie bialgebroid of Poisson groupoid      448
Lie bialgebroid triangular      455
Lie bialgebroid, double of      471
Lie bialgebroid, morphism of      454
Lie derivation law      272 275
Lie derivative      261
Lie derivative of multisections      307
Lie functor      125
Lie group bundle      11
Lie group bundle, gauge      11
Lie group bundle, inner      11 20
Lie pseudoalgebra      144 177
Lie Rinehart algebra      145 308
Lie subalgebroid      164
Lie subalgebroid, restriction      165
Lie subalgebroid, wide      109
Lift, within Lie algebroid coupling      273
Linearization of groupoid action      169
Local system of coefficients      226
Local triviality of Lie algebroid      205 317
Local triviality of Lie groupoid      15 50
Locally constant morphism      240
Locally constant rank      240
Maurer — Cartan equation      101 164 182 191
Monodromy bundle      214
Monodromy groupoid      214 216
Monodromy projection      214
Morphism induced on bisections      27
Morphism of Atiyah sequences induced      98
Morphism of LABs      104
Morphism of LGBs      11
Morphism of Lie algebroids      158
Morphism of Lie algebroids base-preserving      100
Morphism of Lie algebroids induced      124 160
Morphism of Lie algebroids over      100
Morphism of Lie algebroids, action      176
Morphism of Lie groupoids      12
Morphism of Lie groupoids base preserving      12
Morphism of Lie groupoids covering      51
Morphism of Lie groupoids local      217
Morphism of Lie groupoids, action      38 82
Morphism of Poisson groupoids      428
Morphism of principal bundles produced      21
Multisection      304
Multivector field right-invariant      412
Neighbourhood symmetric $\alpha$-      31
Normal subgroupoid system      70
Normal subgroupoid system uniform      76
Object      4
Object inclusion map      4
Obstruction class of Lie algebroid coupling      277
Obstruction cocvcle for Lie algebroid coupling      274
Obstruction to lifting of structure group      331
Orbit      34
Orbit partition      33
Orbit transitivity      32
OUTLINE      341
Pairing of double vector bundles      353
Parallel section      236
Parallel translation      234
Path connection      228
Path connection produced      233
PBG-groupoid      80
PBG-Lie algebroid      173
Pith      37 468
Poisson action      467
Poisson codifferential      406
Poisson cohomology      387
Poisson homology      406
Poisson map      385
Poisson map complete      405
Poisson structure      382
Poisson structure induced by Lie bialgebroid      453
Poisson structure linear      389
Poisson structure linearized      398 405
Poisson structure opposite      399
Poisson structure regular      387
Poisson structure semi-direct      393
Poisson structure, symplectic leaves of      387
Poisson structure, tangent lift      395
Poisson structure, tangent prolongation of      395
Poisson submanifold      385
Poisson vector bundle      xvii 389
Poisson — Lie group      410
Principal bundle      9
Principal bundle produced      21 50
Pseudogroup of local bisections      27
Pullback of Lie algebroid      157
Pullback of Lie groupoid      64
Pullback of vector bundle      54
Quotient of Lie algebroid      168
Quotient of Lie groupoid      73
Quotient of vector bundle      57 58
Quotient of vector bundle over group action      87
Realization of Poisson manifold      xvi143
Reduction      41
Reduction connected      30 51
Reduction of Lie algebroid      109
Relation      401
Relation dual      402
Representation of a Lie algebroid      107
Representation of a Lie algebroid central      273
Representation of a Lie algebroid derivative      172
Representation of a Lie algebroid induced      137
Representation of a Lie algebroid trivial      108
Representation of Lie groupoid      43
Restriction      259
Restriction map      290
Restriction of extension      290
Restriction of Lie algebroid      165
Restriction of Lie groupoid      14
Retroversal      266 277
Reversal isomorphism      361 137
Reverse, of a path      8
Right-translation      5 24
Right-translation local      25
Schouten algebra      304
Section A-parallel      254
Section admissible      50
Section atlas      16
Section core of $\mathcal{VB}$ groupoid      417
Section core of double vector bundle      347
Section decomposing      16
Section linear      389
Section projectable      60
Semi-linear isomorphism      51
Semidirect product of Lie algebroids      270
Semidirect product, general of groupoids      84
Semidirect product, general of Lie algebroids      173
Semidirect product, general of Lie groupoids      78
Set-groupoid      5
Side bundle      340
Source projection      4
Spectral sequence of transitive Lie algebroid      288
Spectral sequence of van Est      334
Splitting of exact sequence of vector bundles      187
Splitting of fibration of Lie algebroids      171
Splitting of fibration of Lie groupoids      79
Standard complex      260
Star      49
Structure equation      200
Subbundle system      58
Subgroupoid base      14
Subgroupoid identity      14
Subgroupoid identity-component      29
Subgroupoid inner      14
Subgroupoid Lie      13
Subgroupoid Lie embedded      14
Subgroupoid Lie locally trivial      41
Subgroupoid Lie wide      14
Subgroupoid normal      60
Subgroupoid stabilizer      10
Submanifold coisotropic      398
Submanifold Lagrangian      429
Submanifold Poisson      385
Submanifold transversal, of base      34
Svstem of local data      211
Symplectic structure      386
System of transition data      318
Tangent pairing      117
Target projection      4
Test case      211
Torsion of Koszul connection in Lie algebroid      154
Transition forms      206 318
Transitivity component      32
Transversal      266 277
Transversal back      309
Transversal flat      266
Tulczyjew isomorphism      364 394
Tulczyjew isomorphism groupoid      134
Unity      5
Vector bundle Poisson, xvii      xvii 389
Vector bundle, Hermitian line      314
Vector bundle, tangent prolongation of      110
Vector field affine      377
Vector field Hamiltonian      383
Vector field homological      177
Vector field left-invariant      131
Vector field linear      113
Vector field multiplicative      372
Vector field right invariant $\beta$-saturated      121
Vector field right invariant local      123
Vector field vertical      120
Vector field, complete lift of      119
Vector field, right invariant      120
Vector field, star      375 379
Vector field, vertical lift      112
Versal      66 83
Vertex bundle      17
Vertex group      5 49
Vertical bundle of a double vector bundle      341
Vertical bundle of a submersion      36
Weak pullback      83
Zero double      341
Сhange of Lie algebroids      289
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