1 |
D Arnal, M
Cahen, S Gutt, Deformations
on coadjoint orbits, J. Geom. Phys. 3 (1986)
327–351 MR894630 |
2 |
D Arnal, J
Ludwig, M Masmoudi, Déformations
covariantes sur les orbites polarisées d'un groupe de
Lie, J. Geom. Phys. 14 (1994) 309–331 MR1303958 |
3 |
D Arnal, D
Manchon, M Masmoudi, Choix des signes
pour la formalite de M Kontsevich, Pacific J.
Math. 202 (2002) 23–66 |
4 |
F Bayen, M
Flato, C Fronsdal, A Lichnerowicz, D
Sternheimer, Quantum mechanics as a
deformation of classical mechanics, Lett. Math. Phys. 1
(1975/77) 521–530 MR0674337 |
5 |
M Bertelson,
Equivalence de produits star, Mémoire de Licence,
Université Libre de Bruxelles (1995) |
6 |
M Bertelson, P
Bieliavsky, S Gutt, Parametrizing
equivalence classes of invariant star products, Lett.
Math. Phys. 46 (1998) 339–345 MR1668581 |
7 |
M Bertelson, M
Cahen, S Gutt, Equivalence of
star products, Classical Quantum Gravity 14 (1997)
MR1691889 |
8 |
M Bordemann,
(Bi)modules, morphismes et réduction des star-produits:
le cas symplectique, feuilletages et obstructions arXiv:math.QA/0403334 |
9 |
M Bordemann,
Deformation quantization: a mini-lecture, from:
"Geometric and topological methods for quantum field theory",
Contemp. Math. 434, Amer. Math. Soc. (2007) 3–38 MR2349629 |
10 |
N Bourbaki,
Éléments de mathématique. Fasc XXXVII:
Groupes et algèbres de Lie. Chapitre II: Algèbres de
Lie libres. Chapitre III: Groupes de Lie, Actualités
Scientifiques et Industrielles 1349, Hermann (1972) 320
MR0573068 |
11 |
A Bruyère, A
Cattaneo, B Keller, C Torossian,
Déformation, quantification, théorie de Lie,
Panoramas et Synthèse 20 (1995) |
12 |
M Cahen, S
Gutt, Produits \star sur les espaces affins
symplectiques localement symétriques, C. R. Acad. Sci.
Paris Sér. I Math. 297 (1983) 417–420 MR732848 |
13 |
M Cahen, S
Gutt, Produits \star sur les orbites des groupes
semi-simples de rang 1, C. R. Acad. Sci. Paris Sér. I
Math. 296 (1983) 821–823 MR711840 |
14 |
M Cahen, S
Gutt, An algebraic construction of ∗ product on
the regular orbits of semisimple Lie groups, from:
"Gravitation and geometry", Monogr. Textbooks Phys. Sci. 4,
Bibliopolis (1987) 71–82 MR938533 |
15 |
M Cahen, S
Gutt, M De Wilde, Local cohomology of the
algebra of C∞ functions on a connected
manifold, Lett. Math. Phys. 4 (1980) 157–167
MR583079 |
16 |
M Cahen, S
Gutt, J Rawnsley, On
tangential star products for the coadjoint Poisson
structure, Comm. Math. Phys. 180 (1996) 99–108
MR1403860 |
17 |
A S Cattaneo,
Formality and star products, from: "Poisson geometry,
deformation quantisation and group representations", London
Math. Soc. Lecture Note Ser. 323, Cambridge Univ. Press (2005)
79–144 MR2166452
Lecture notes taken by D Indelicato |
18 |
A S Cattaneo,
G Felder, On the globalization of Kontsevich's star
product and the perturbative Poisson sigma model, Progr.
Theoret. Phys. Suppl. (2001) 38–53 MR2023844
Noncommutative geometry and string theory (Yokohama, 2001) |
19 |
A S Cattaneo,
G Felder, L Tomassini, From local to
global deformation quantization of Poisson manifolds,
Duke Math. J. 115 (2002) 329–352 MR1944574 |
20 |
A Connes,
Noncommutative differential geometry, Inst. Hautes
Études Sci. Publ. Math. (1985) 257–360 MR823176 |
21 |
M De Wilde,
Deformations of the algebra of functions on a symplectic
manifold: a simple cohomological approach, publication
96.005, Institut de Mathématique, Université de
Liége (1996) |
22 |
M De Wilde,
P B A Lecomte, Existence of
star-products and of formal deformations of the Poisson Lie
algebra of arbitrary symplectic manifolds, Lett. Math.
Phys. 7 (1983) 487–496 MR728644 |
23 |
M De Wilde, P
Lecomte, S Gutt, À propos des deuxième
et troisième espaces de cohomologie de l'algèbre de
Lie de Poisson d'une variété symplectique, Ann.
Inst. H. Poincaré Sect. A (N.S.) 40 (1984) 77–83
MR745682 |
24 |
P Deligne, Déformations de
l'algèbre des fonctions d'une variété
symplectique: comparaison entre Fedosov et De Wilde,
Lecomte, Selecta Math. (N.S.) 1 (1995) 667–697
MR1383583 |
25 |
V Dolgushev,
Covariant and
equivariant formality theorems, Adv. Math. 191 (2005)
147–177 MR2102846 |
26 |
V G Drinfel'd,
Quantum groups, from: "Proceedings of the International
Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif.,
1986)", Amer. Math. Soc. (1987) 798–820 MR934283 |
27 |
B V Fedosov,
A
simple geometrical construction of deformation
quantization, J. Differential Geom. 40 (1994)
213–238 MR1293654 |
28 |
B Fedosov,
Deformation quantization and index theory, Mathematical
Topics 9, Akademie Verlag (1996) 325 MR1376365 |
29 |
R Fioresi, M A
Lledó, On the deformation quantization of coadjoint
orbits of semisimple groups, Pacific J. Math. 198 (2001)
411–436 MR1835516 |
30 |
M Flato,
Deformation view of physical theories, Czech J. Phys.
B32 (1982) 472–475 |
31 |
M Flato, A
Lichnerowicz, D Sternheimer, Crochet de
Moyal–Vey et quantification, C. R. Acad. Sci. Paris
Sér. A-B 283 (1976) MR0426048 |
32 |
M Gerstenhaber,
On the
deformation of rings and algebras, Ann. of Math. (2) 79
(1964) 59–103 MR0171807 |
33 |
S Gutt, Equivalence of
deformations and associated ∗ –products,
Lett. Math. Phys. 3 (1979) 297–309 MR545408 |
34 |
S Gutt, Second et
troisième espaces de cohomologie différentiable de
l'algèbre de Lie de Poisson d'une variété
symplectique, Ann. Inst. H. Poincaré Sect. A (N.S.) 33
(1980) 1–31 MR593022 |
35 |
S Gutt, An explicit ^∗
–product on the cotangent bundle of a Lie group,
Lett. Math. Phys. 7 (1983) 249–258 MR706215 |
36 |
S Gutt, On some second
Hochschild cohomology spaces for algebras of functions on a
manifold, Lett. Math. Phys. 39 (1997) 157–162
MR1437749 |
37 |
S Gutt, J
Rawnsley, Equivalence
of star products on a symplectic manifold; an introduction to
Deligne's \v Cech cohomology classes, J. Geom. Phys. 29
(1999) 347–392 MR1675581 |
38 |
A V Karabegov,
Cohomological
classification of deformation quantizations with separation of
variables, Lett. Math. Phys. 43 (1998) 347–357
MR1620745 |
39 |
M Kontsevich,
Deformation
quantization of Poisson manifolds, Lett. Math. Phys. 66
(2003) 157–216 MR2062626 |
40 |
A Lichnerowicz,
Existence and
equivalence of twisted products on a symplectic
manifold, Lett. Math. Phys. 3 (1979) 495–502
MR555333 |
41 |
A Lichnerowicz,
Déformations
d'algèbres associées à une variété
symplectique (les \astν
–produits), Ann. Inst. Fourier (Grenoble) 32
(1982) 157–209 MR658948 |
42 |
M Masmoudi,
Tangential
formal deformations of the Poisson bracket and tangential star
products on a regular Poisson manifold, J. Geom. Phys.
9 (1992) 155–171 MR1166720 |
43 |
F Nadaud, On continuous and
differential Hochschild cohomology, Lett. Math. Phys.
47 (1999) 85–95 MR1669382 |
44 |
R Nest, B
Tsygan, Algebraic index
theorem for families, Adv. Math. 113 (1995)
151–205 MR1337107 |
45 |
N Neumaier,
Local
ν–Euler derivations and Deligne's characteristic
class of Fedosov star products and star products of special
type, Comm. Math. Phys. 230 (2002) 271–288 |
46 |
H Omori, Y
Maeda, A Yoshioka, Weyl manifolds
and deformation quantization, Adv. Math. 85 (1991)
224–255 MR1093007 |
47 |
H Omori, Y
Maeda, A Yoshioka, The uniqueness of
star-products on Pn(C), from:
"Differential geometry (Shanghai, 1991)", World Sci. Publ.,
River Edge, NJ (1993) 170–176 MR1341610 |
48 |
G Pinczon, On the equivalence
between continuous and differential deformation
theories, Lett. Math. Phys. 39 (1997) 143–156
MR1437748 |
49 |
D Rauch,
Equivalence de produits star et classes de Deligne,
Mémoire de Licence, Université Libre de Bruxelles
(1998) |
50 |
D Sternheimer,
Deformation quantization: twenty years after, from:
"Particles, fields, and gravitation (Lódź, 1998)",
AIP Conf. Proc. 453, Amer. Inst. Phys. (1998) 107–145
MR1765495 |
51 |
D Tamarkin, Another
proof of M Kontsevich formality theorem arXiv:math/9803025 |
52 |
D Tamarkin,
Formality of chain operad of small squares arXiv:math/9809164 |
53 |
J Vey, Déformation du
crochet de Poisson sur une variété
symplectique, Comment. Math. Helv. 50 (1975)
421–454 MR0420753 |
54 |
S Waldmann,
States
and representations in deformation quantization, Rev.
Math. Phys. 17 (2005) 15–75 MR2130623 |
55 |
A Weinstein, P
Xu, Hochschild cohomology and characteristic classes for
star-products, from: "Geometry of differential equations",
Amer. Math. Soc. Transl. Ser. 2 186, Amer. Math. Soc. (1998)
177–194 MR1732412 |