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Izu Vaisman — Lectures on the geometry of Poisson manifolds
Izu Vaisman — Lectures on the geometry of Poisson manifolds

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Название: Lectures on the geometry of Poisson manifolds

Автор: Izu Vaisman

Аннотация:

This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 1994

Количество страниц: 220

Добавлена в каталог: 01.11.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action, Hamiltonian      107
Action, infinitesimal      107
Action, of a Lie group      107
Action, Poisson      107
Affine Poisson groups      166
Almost-symplectic manifold      36
Anchor map      148
Annihilator      37
Bi-cross section      146
Bi-cross section, Lagrangian      146
Bohr — Sommerfeld condition      88
Bracket, Jacobi      3
Bracket, Poisson      1
Canonical coordinates      29
Casimir functions      30
Central extension      35
Characteristic (Chern) class of the isotropic realization      130
Characteristic form-class      131
Chevalley-Eilenberg cohomology      90
Clean intersection      99
Cofoliation      54
Coisotrjdpic submanifold      99
Contact manifold      36
Contravariant derivative      55
Deformation      93
Differential, contravariant exterior      43
Dirac bracket      37
Distinguished cross section      126
Distribution, characteristic      19
Distribution, completely integrable      20
Distribution, differentiable      19
Distribution, general      19
Distribution, invariant      20
Distribution, involutive      21
Distribution, leaf of completely integrable      20
Distribution, rank of      19
Distribution, regular      19
Distribution, subcharacteristic      104
Divergence, generalized      12
Double Lie algebra      187
Double Lie group      187
Dressing transformations      185
Dressing vector field      185
Dual group      185
Foliation, general      20
Foliation, leafwise symplectic      36
Foliation, Libermann      115
Foliation, regular      20
Foliation, symplectically complete      115
Function group      121
Function group, polar      121
Gauge groupoid      140
Groupoid      138
Groupoid, banal      138
Groupoid, double symplectic      144
Groupoid, homomorphism      144
Groupoid, local symplectic      151
Groupoid, symplectic      143
Groupoid, transitive      139
Groupoid, zero      139
Hamiltonian vector field      5
Heisenberg-Poisson (HP) manifold      153
Hochschild cohomology      94
Hochschild cohomology, z-vector      6
Intrinsic derivative      166
Isotropic realizations      123
Isotropic realizations, connected complete (c.c.i.)      124
Isotropic realizations, Libermann      124
Jacobian cocycle      169
Lagrangian submanifold      100
Legendrian submanifold      155
Libermann foliation      54
Lichnerowicz-Poisson cohomology      63
Lie algebra cohomology      90
Lie algebroid      43 148
Lie bialgebra      170
Lie bigebra      170
Lie groupoid      140
Lie groupoid, local      150
Lie — Drinfeld algebra      169
Lie — Poisson structure      32
Linear approximation      34
Local Lie algebra      3
LP — Poincare lemma      75
LP-simple neighbourhood      75
Manifold, contact      3
Manifold, Dirac      3
Manifold, Jacobi      3 17
Manifold, locally conformal symplectic      3
Manifold, Poisson      2
Manifold, symplectic      6
Manin triple      178
Mayer — Vietoris exact sequence      65
Momentum map      109
Momentum map, equivariant      109
Multiplicative tensor field      162
Net      128 129
Observables      83 93
Orbit      139
Phase space      83
Point, regular      19
Point, singular      19
Poisson action      182
Poisson algebra      1
Poisson automorphism      16 97
Poisson automorphism, infinitesimal      26
Poisson bivector      5
Poisson characteristic classes      85
Poisson codifferential      45
Poisson connection      11 29
Poisson equivalence      16 97
Poisson homology      77
Poisson isomorphism      97
Poisson manifold      2
Poisson manifold, exact      63
Poisson manifold, integrable      150
Poisson manifold, quantizable      86
Poisson manifold, reduced      102
Poisson manifold, regular      27
Poisson manifolds, dual      121
Poisson mapping      16
Poisson morphism      16 97
Poisson product      17
Poisson relation      100
Poisson space      2
Poisson structure, affine      34
Poisson structure, coinduced      98
Poisson structure, constant      31
Poisson structure, linear      31
Poisson structure, linearizable      34
Poisson structure, nondegenerate      26
Poisson structure, quadratic      35
Poisson structure, rank of      26
Poisson structure, reduced      106
Poisson structure, transverse      29
Poisson structures, compatible      15
Poisson submanifold      16
Poisson — Chem classes      85
Poisson — Godbillon — Vey class      64
Poisson — Lie algebra      169
Poisson — Lie group      161
Poisson — Lie subgroup      183
Poisson — Nijenhuis structure      62
Polarization      87
Prequantization      83
Prequantization bundle      84
Prequantization formula      84
Prequantization representation      89
Product, interior      13
Product, Poisson      17
Quantization      83 87
Quantization, deformation      83 92
Quantization, geometric      83
Quasi — Poisson — Lie groups      188
Realizations, equivalent      119
Reducibility condition      103
Reducible triple      102
Reduction      101
Reduction, leafwise      104
Reductive structure      102
Representation, adjoint      32
Representation, coadjoint      33
Schouten bracket, algebraic      172
Schouten — Nijenhuis bracket      9
Schouten-Nijenhuis bracket, covariant      59
Set of units      139
Splitting theorem      27
Symbol      89
Symplectic connection      16
Symplectic connections      29
Symplectic foliation      26
Symplectic leaves      26
Symplectic realization      115
Theorem, generalized Frobenius      25
Theorem, Noether’s      114
Theorem, Sussmann — Stefan — Frobenius      20
Theorem, Viflyantsev — Frobenius      21
Triangular Poisson — Lie algebra      173
Twilled Lie algebra      187
Unit submanifold      140
Vanishing cycle      157
Yang-Baxter (YB) equation, classical      173
Yang-Baxter equation, groupgeneralized classical (GYB)      173
Yang-Baxter equation, modified (MYB)      176
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