| 1 |
M Adler, P van
Moerbeke, P Vanhaecke, Algebraic completely
integrable systems, Painlevé architecture and Lie
algebras, Springer (2004) |
| 2 |
V I Arnol'd,
Remarks on Poisson structures on a plane and on other powers
of volume elements, Trudy Sem. Petrovsk. (1987)
37–46, 242 MR933050 |
| 3 |
V I Arnol'd,
Geometrical methods in the theory of ordinary differential
equations, Grundlehren der Mathematischen Wissenschaften
250, Springer (1988) MR947141
Translated from the Russian by Joseph Szücs |
| 4 |
M Audin, Spinning
tops, Cambridge Studies in Advanced Mathematics 51,
Cambridge University Press (1996) MR1409362
A course on integrable systems |
| 5 |
O Babelon, D
Bernard, M Talon, Introduction to
classical integrable systems, Cambridge Monographs on
Mathematical Physics, Cambridge University Press (2003)
MR1995460 |
| 6 |
A V Bolsinov,
A T Fomenko, Integriruemye gamiltonovy sistemy.
1, 2, Izdatel'skiĭ Dom “Udmurtskiĭ
Universitet”, Izhevsk (1999) MR1792190
Geometriya, topologiya, klassifikatsiya, Appendices 2 and 3 by
V V Kalashnikov, Jr |
| 7 |
M Bordemann, A
Makhlouf, T Petit, Déformation
par quantification et rigidité des algèbres
enveloppantes, J. Algebra 285 (2005) 623–648
MR2125456 |
| 8 |
R Bott, L W
Tu, Differential forms in algebraic topology,
Graduate Texts in Mathematics 82, Springer (1982) MR658304 |
| 9 |
N Bourbaki,
Éléments de mathématique XXVI: Groupes et
algèbres de Lie. Chapitre 1: Algèbres de Lie,
Actualités Sci. Ind. 1285, Hermann, Paris (1960) MR0132805 |
| 10 |
R Carles, Sur la
structure des algèbres de Lie rigides, Ann. Inst.
Fourier (Grenoble) 34 (1984) 65–82 MR762694 |
| 11 |
R Carles,
Déformations et éléments nilpotents dans les
schémas définis par les identités de Jacobi,
C. R. Acad. Sci. Paris Sér. I Math. 312 (1991)
671–674 MR1105623 |
| 12 |
C Chevalley, S
Eilenberg, Cohomology theory of Lie
groups and Lie algebras, Trans. Amer. Math. Soc. 63
(1948) 85–124 MR0024908 |
| 13 |
V Chloup-Arnould,
Linearization
of some Poisson–Lie tensor, J. Geom. Phys. 24
(1997) 46–52 MR1486708 |
| 14 |
J F Conn,
Normal forms for
analytic Poisson structures, Ann. of Math. (2) 119
(1984) 577–601 MR744864 |
| 15 |
J F Conn,
Normal forms for
smooth Poisson structures, Ann. of Math. (2) 121 (1985)
565–593 MR794374 |
| 16 |
M Crainic, Differentiable
and algebroid cohomology, van Est isomorphisms, and
characteristic classes, Comment. Math. Helv. 78 (2003)
681–721 MR2016690 |
| 17 |
M Crainic, R L
Fernandes, Lectures on
integrability of Lie brackets, from: "Lectures on
Poisson Geometry", Geom. Topol. Monogr. 17, Geometry &
Topology Publications (2010) 1–107 |
| 18 |
P Dazord,
Stabilité et linéarisation dans les
variétés de Poisson, from: "Symplectic geometry
and mechanics (Balaruc, 1983)", Travaux en Cours, Hermann
(1985) 59–75 MR848743 |
| 19 |
L A Dickey,
Soliton equations and Hamiltonian systems, Advanced
Series in Mathematical Physics 26, World Scientific Publishing
Co. (2003) MR1964513 |
| 20 |
J P Dufour,
Linéarisation
de certaines structures de Poisson, J. Differential
Geom. 32 (1990) 415–428 MR1072912 |
| 21 |
J P Dufour, M
Zhitomirskii, Classification of
nonresonant Poisson structures, J. London Math. Soc.
(2) 60 (1999) 935–950 MR1753824 |
| 22 |
J P Dufour,
N T Zung, Nondegeneracy
of the Lie algebra aff(n), C. R. Math. Acad.
Sci. Paris 335 (2002) 1043–1046 MR1955585 |
| 23 |
J P Dufour,
N T Zung, Poisson structures and their normal
forms, Progress in Mathematics 242, Birkhäuser Verlag
(2005) MR2178041 |
| 24 |
I M Gel'fand,
I Y Dorfman, Hamiltonian operators and the
classical Yang–Baxter equation, Funktsional. Anal. i
Prilozhen. 16 (1982) 1–9, 96 MR684122 |
| 25 |
V L Ginzburg,
Momentum mappings
and Poisson cohomology, Internat. J. Math. 7 (1996)
329–358 MR1395934 |
| 26 |
V L Ginzburg,
Equivariant
Poisson cohomology and a spectral sequence associated with a
moment map, Internat. J. Math. 10 (1999) 977–1010
MR1739368 |
| 27 |
V L Ginzburg,
Grothendieck
groups of Poisson vector bundles, J. Symplectic Geom. 1
(2001) 121–169 MR1959580 |
| 28 |
V L Ginzburg,
A Golubev, Holonomy on Poisson
manifolds and the modular class, Israel J. Math. 122
(2001) 221–242 MR1826501 |
| 29 |
V L Ginzburg,
J H Lu, Poisson
cohomology of Morita-equivalent Poisson manifolds,
Internat. Math. Res. Notices (1992) 199–205 MR1191570 |
| 30 |
V L Ginzburg,
A Weinstein, Lie–Poisson structure
on some Poisson Lie groups, J. Amer. Math. Soc. 5
(1992) 445–453 MR1126117 |
| 31 |
M Goze, J M
Ancochea Bermudez, On the
classification of rigid Lie algebras, J. Algebra 245
(2001) 68–91 MR1868184 |
| 32 |
V Guillemin, E
Lerman, S Sternberg, Symplectic fibrations and
multiplicity diagrams, Cambridge University Press (1996)
MR1414677 |
| 33 |
V W Guillemin,
S Sternberg, Remarks on a paper of
Hermann, Trans. Amer. Math. Soc. 130 (1968)
110–116 MR0217226 |
| 34 |
R Hermann, The formal linearization of
a semisimple Lie algebra of vector fields about a singular
point, Trans. Amer. Math. Soc. 130 (1968) 105–109
MR0217225 |
| 35 |
G Hochschild,
J P Serre, Cohomology of Lie
algebras, Ann. of Math. (2) 57 (1953) 591–603
MR0054581 |
| 36 |
D Holm, Applications of
Poisson geometry to physical problems, from: "Lectures
on Poisson Geometry", Geom. Topol. Monogr. 17, Geometry &
Topology Publications (2010) 221–384 |
| 37 |
J Huebschmann,
Poisson
cohomology and quantization, J. Reine Angew. Math. 408
(1990) 57–113 MR1058984 |
| 38 |
N Jacobson, Lie
algebras, Interscience Tracts in Pure and Applied
Mathematics 10, Interscience Publishers, New York-London (1962)
MR0143793 |
| 39 |
M V Karasëv,
Analogues of objects of the theory of Lie groups for
nonlinear Poisson brackets, Izv. Akad. Nauk SSSR Ser. Mat.
50 (1986) 508–538, 638 MR854594 |
| 40 |
A A Kirillov,
Lectures on the orbit method, Graduate Studies in
Mathematics 64, American Mathematical Society (2004) MR2069175 |
| 41 |
M Kontsevich,
Deformation
quantization of Poisson manifolds, Lett. Math. Phys. 66
(2003) 157–216 MR2062626 |
| 42 |
J L Koszul,
Crochet de Schouten–Nijenhuis et cohomologie,
Astérisque (1985) 257–271 MR837203
The mathematical heritage of Élie Cartan (Lyon, 1984) |
| 43 |
A G
Kušnirenko, An analytic action of a semisimple Lie
group in a neighborhood of a fixed point is equivalent to a
linear one, Funkcional. Anal. i Priložen 1 (1967)
103–104 MR0210833 |
| 44 |
A Lichnerowicz,
Les
variétés de Poisson et leurs algèbres de Lie
associées, J. Differential Geometry 12 (1977)
253–300 MR0501133 |
| 45 |
J H Lu,
Momentum mappings and reduction of Poisson actions,
from: "Symplectic geometry, groupoids, and integrable systems
(Berkeley, CA, 1989)", Math. Sci. Res. Inst. Publ. 20, Springer
(1991) 209–226 MR1104930 |
| 46 |
J H Lu,
Poisson
homogeneous spaces and Lie algebroids associated to Poisson
actions, Duke Math. J. 86 (1997) 261–304 MR1430434 |
| 47 |
E Miranda, N T
Zung, A note on equivariant normal forms of Poisson
structures, Math. Res. Lett. 13 (2006) 1001–1012
MR2280793 |
| 48 |
A S
Miščenko, A T Fomenko, Euler
equation on finite-dimensional Lie groups, Izv. Akad. Nauk
SSSR Ser. Mat. 42 (1978) 396–415, 471 MR0482832 |
| 49 |
J C Molinier,
Linéarisation de structures de Poisson, thèse,
Montpellier (1993) |
| 50 |
P Monnier, Poisson cohomology in
dimension two, Israel J. Math. 129 (2002) 189–207
MR1910942 |
| 51 |
P Monnier, N T
Zung, Levi
decomposition for smooth Poisson structures, J.
Differential Geom. 68 (2004) 347–395 MR2144250 |
| 52 |
J Moser, On the volume elements on a
manifold, Trans. Amer. Math. Soc. 120 (1965)
286–294 MR0182927 |
| 53 |
A Nijenhuis,
Jacobi-type identities for bilinear differential
concomitants of certain tensor fields I, II, Indag. Math.
17 (1955) 390–397, 398–403 MR0074879 |
| 54 |
A Nijenhuis,
R W Richardson Jr., Cohomology
and deformations in graded Lie algebras, Bull. Amer.
Math. Soc. 72 (1966) 1–29 MR0195995 |
| 55 |
A Odzijewicz,
Hamiltonian and
Quantum Mechanics, from: "Lectures on Poisson
Geometry", Geom. Topol. Monogr. 17, Geometry & Topology
Publications (2010) 385–472 |
| 56 |
A Pichereau,
Poisson
(co)homology and isolated singularities, J. Algebra 299
(2006) 747–777 MR2228339 |
| 57 |
R W Richardson
Jr., On
the rigidity of semi-direct products of Lie algebras,
Pacific J. Math. 22 (1967) 339–344 MR0212061 |
| 58 |
J A Schouten,
Ueber Differentialkomitanten zweier kontravarianter
Grössen, Nederl. Akad. Wetensch., Proc. 43 (1940)
449–452 MR0003324 |
| 59 |
J A Schouten,
On the differential operators of first order in tensor
calculus, from: "Convegno Internazionale di Geometria
Differenziale, Italia, 1953", Edizioni Cremonese (1954)
1–7 MR0063750 |
| 60 |
P Stefan, Accessible sets,
orbits, and foliations with singularities, Proc. London
Math. Soc. (3) 29 (1974) 699–713 MR0362395 |
| 61 |
H J Sussmann,
Orbits of
families of vector fields and integrability of
distributions, Trans. Amer. Math. Soc. 180 (1973)
171–188 MR0321133 |
| 62 |
I Vaisman, Lectures
on the geometry of Poisson manifolds, Progress in
Mathematics 118, Birkhäuser Verlag (1994) MR1269545 |
| 63 |
V S Varadarajan,
Lie groups, Lie algebras, and their representations,
Graduate Texts in Mathematics 102, Springer (1984) MR746308
Reprint of the 1974 edition |
| 64 |
Y Vorobjev,
Coupling tensors and Poisson geometry near a single
symplectic leaf, from: "Lie algebroids and related topics
in differential geometry (Warsaw, 2000)", Banach Center Publ.
54, Polish Acad. Sci. (2001) 249–274 MR1881658 |
| 65 |
A Wade, Normalisation
formelle de structures de Poisson, C. R. Acad. Sci.
Paris Sér. I Math. 324 (1997) 531–536 MR1443989 |
| 66 |
A Wade, N T
Zung, Poisson geometry of Frobenius Lie algebras, in
preparation (2003) |
| 67 |
A Weinstein,
Lectures on symplectic manifolds, American Mathematical
Society (1977) MR0464312
Expository lectures from the CBMS Regional Conference held at
the University of North Carolina, March 8–12, 1976,
Regional Conference Series in Mathematics, No. 29 |
| 68 |
A Weinstein,
The
local structure of Poisson manifolds, J. Differential
Geom. 18 (1983) 523–557 MR723816 |
| 69 |
A Weinstein,
Poisson structures and Lie algebras, Astérisque
(1985) 421–434 MR837210
The mathematical heritage of Élie Cartan (Lyon, 1984) |
| 70 |
A Weinstein,
Poisson
geometry of the principal series and nonlinearizable
structures, J. Differential Geom. 25 (1987) 55–73
MR873455 |
| 71 |
A Weinstein,
Symplectic
groupoids and Poisson manifolds, Bull. Amer. Math. Soc.
(N.S.) 16 (1987) 101–104 MR866024 |
| 72 |
A Weinstein, P
Xu, Extensions of symplectic groupoids and
quantization, J. Reine Angew. Math. 417 (1991)
159–189 MR1103911 |
| 73 |
P Xu, Poisson
cohomology of regular Poisson manifolds, Ann. Inst.
Fourier (Grenoble) 42 (1992) 967–988 MR1196101 |
| 74 |
N T Zung,
Levi
decomposition of analytic Poisson structures and Lie
algebroids, Topology 42 (2003) 1403–1420 MR1981362 |
| 75 |
N T Zung,
Proper
groupoids and momentum maps: linearization, affinity, and
convexity, Ann. Sci. École Norm. Sup. (4) 39
(2006) 841–869 MR2292634 |
