next up previous contents
Next: About this document ... Up: From Poisson to Quantum Previous: Coisotropic creed   Contents

Bibliography

1
Abouqateb A. and Boucetta M., The modular class of a regular Poisson manifold and the Reeb class of its symplectic foliation. C.R.Math Acad. Sci. Paris 337, 61-66 (2003).

2
Aminou R. and Kosmann-Schwarzbach Y., Bigébres de Lie doubles et carrés, Ann. Inst. H.Poincaré, Phys.Teor. 49A, 461-478 (1988).

3
Belavin A.A. e Drinfel'd V.G., Solutions of the classical Yang-Baxter equation for simple Lie algebras, Funct. Anal. Appl. 16, 159-180 (1982).

4
Benayed M., Central extensions of Lie bialgebras and Poisson-Lie groups, Journ. Geom. Phys. 16, 301-304 (1995).

5
Benayed M., Lie bialgebras real cohomology, Journ. Lie Theory 7, 287-292 (1997).

6
Bonechi F., Ciccoli N. and Tarlini M., Non commutative instantons on the 4-sphere from quantum groups, Commun. Math. Phys. 226, 419-432 (2002).

7
Bonechi F., Ciccoli N. and Tarlini M., Quantum even spheres $\Sigma^{2n}_q$ from Poisson double suspension, Commun. Math. Phys. 234, 449-459 (2003).

8
Bonechi F., Ciccoli N., L. Dabrowski and Tarlini M., Bijectivity of the canonical map for the non commutative instanton bundle, Journ. Geom. Phys. 51, 71-81 (2004).

9
Bordermann M. Nondegenerate invariant bilinear forms on non associative algebras Acta Math. Univ. Comen. 66, 151-201 (1997).

10
Brylinski J.-L., A differential complex for Poisson manifolds, J. Diff. Geom. 28, 93-114 (1998).

11
J.-L. Brylinski e E. Geztler., The homology of algebras of pseudo-differential symbols and the non commutative residue, K-theory 1, 385-402 (1987).

12
Bursztyn H. and Radko O., Gauge equivalence of Dirac structures and symplectic groupoids, Ann. Inst. Fourier (Grenoble) 53, 309-337 (2003).

13
Bursztyn H. and Weinstein A., Poisson geometry and Morita equivalence, math.SG/0402347.

14
Bursztyn H. and Weinstein A., Picard groups in Poisson geometry, Moscow J. Math.....

15
Canas da Silva A. e Weinstein A., Geometric models for Noncommutative Algebras, Berkeley Mathematics Lectures vol. 10, American Mathematical Society, Providence 1999.

16
A. Cattaneo and G. Felder, Coisotropic submanifolds in Poisson geometry, branes and Poisson $\sigma$-models, Lett. Math. Phys. 69 (2004), 157-175.

17
Chari V. and Pressley A., A guide to quantum groups, Cambridge University Press, Cambridge 1994.

18
Ciccoli N. and Gavarini F., Quantum duality principle for coisotropic subgroups and quotients, Adv. Math. 199, 104-135 (2006).

19
Ciccoli N. e Guerra L., Lagrangian subalgebra of the double $Sl(2,\mathbb R)$, Geom. Ded. in stampa.

20
Ciccoli N. and Sheu A.J.-L., Covariant Poisson structures on complex Grassmannians, Comm. Anal. Geom. at press.

21
Crainic M., Differentiable and algebroid cohomology, van Est isomorphisms and characteristic classes, Comment. Math. Helv. 78, 681-721 (2003).

22
Crainic M. and Fernandes R.L., Integrability of Poisson brackets, Journ. Diff. Geom. 66, 71-137 (2004).

23
Crainic M. and Fernandes R.L., Rigiditiy and flexibility in Poisson geometry, Trav. Math. 16, 53-68 (2005).

24
Courant T., Dirac manifolds, Trans. Amer. Math. Soc. 319, 631-661(1990).

25
De Smedt V. Existence of a Lie bialgebra structure on every Lie algebra, Lett. Math. Phys. 31, 225-231 (1994).

26
M. S. Dijkhuizen and M. Noumi, A family of quantum projective spaces and related $q$-hypergeometric orthogonal polynomials, Trans. Amer. Math. Soc. 350 (1998), 3269-3296.

27
M.S. Dijkhuizen, M. Noumi and T. Sugitani, Multivariable Askey-Wilson polynomials and quantum complex Grassmannians, in "Special functions, $q$-series and related topics", eds. M.E.H. Ismail et al., 167-177, Fields. Inst. Comm. 14, AMS (1997).

28
Drinfel'd V.G., Hamiltonian Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equation, Sov. Math. Dokl. 27, 68-71 (1983).

29
Drinfel'd V.G., On Poisson homogeneous spaces of Poisson-Lie groups, Teor. Math. Phys. 95, 226-227 (1993).

30
E. Dahl e B. Enriquez, Homologie cyclique et de Hochschild de certaines èspaces homogènes quantiques, K-theory 6, 499-517 (1992).

31
Delorme P., Classification des triples de Manin pour les algébres de Lie réductives complexes. J. Algebra 246, 97-174 (2001).

32
Etingof P. e Varchenko A., Geometry and classification of solutions of the classical dynamical Yang-Baxter equation, Comm. Math. Phys. 192, 77-120 (1998).

33
Evens S. and Lu J.-H., Poisson harmonic forms, Kostant harmonic forms and the $\mathbb S^1$-equivariant cohomology of $K/T$, Adv. Math. 142, 171-220 (1999).

34
S. Evens and J.-H. Lu, On the variety of Lagrangian subalgebras I., Ann. Sci. Ecole Norm. Sup. Paris 34 (2001), 631-668.

35
S. Evens and J.-H. Lu, On the variety of Lagrangian subalgebras II., Ann. Sci. Ecole Norm. Sup. Paris, to appear.

36
Evans S., Lu J.H. and Weinstein A., Transverse measures, the modular class and a cohomology pairing for Lie algebroids, Quart. J. Math. Oxford 50, 417-436 (1999).

32
Etingof P. e Varchenko A., Geometry and classification of solutions of the classical dynamical Yang-Baxter equation, Comm. Math. Phys. 192, 77-120 (1998).

37
P. Feng e B. Tsygan, Hochschild and cyclic homology of quantum groups, Comm. Math. Phys. 140, 481-521 (1990).

38
Feldvöss J., Existence of triangular Lie bialgebra structures, Jour. Pure Appl. Alg. 134, 1-14 (1999).

39
R.L. Fernandes, Connections in Poisson Geometry I: Holonomy and Invariants, J. of Differential Geometry 54, (2000) 303-366.

40
Fernandes R. L., Lie algebroids, holonomy and characteristic classes, Adv. Math. 170, 119-179 (2002).

41
P. Foth and J.-H. Lu, A Poisson structure on compact symmetric spaces, Commun. Math. Phys. 251 (2004), 557-566.

42
B. Fresse, Théorie des opérades de Koszul et homologie des algèbres de Poisson, preprint 1995.

43
Ginzburg V., Momentum mappings and Poisson cohomology, Int. J. Math. 7, 329-358 (1996).

44
V. Ginzburg, Grothendieck groups of Poisson vector bundles, J. Sympl. Geom. 1, 121-169 (2002).

45
Gomez X., Classification of 3-dimensional Lie bialgebras, Journ. Math. Phys. 41, 4939-4956 (2000).

46
Hawkins E., Noncommutative rigidity, Commun. Math. Phys. 246, 211-235 (2004).

47
Ibort A. and Martínez Torres D, A new construction of Poisson manifolds, Journ of Symp. Geom. 2, 83-107 (2003).

48
E. Karolinsky, The classification of Poisson homogeneous spaces of compact Poisson Lie groups, Mathematical Physics, Analysis, and Geometry, 3 (1996), 272-289.

49
S. Khoroshkin, A. Radul, and V. Rubtsov, A family of Poisson structures on hermitian symmetric spaces, Comm. Math. Phys. 152 (1993), 299-315.

50
Koszul J.-L., Crochét de Schouten-Nijenhuis et cohomologie, Astèrisque hors série 257-271 (1985).

51
Liu Z.J. e Qian M., Generalized Yang-Baxter equations, Koszul operators and Poisson-Lie groups, J. Diff. Geom. 35, 399-414 (1992).

52
Liu Z. J., Weinstein A. and Xu P, Manin triples for Lie bialgebroids, J. Diff. Geom. 45, 547-574 (1997).

53
J. H. Lu, Multiplicative and affine Poisson structures on Lie groups, Ph. D. thesis, Univ. of California, Berkeley, 1990.

54
Lu J.-H., Poisson homogeneous spaces and Lie algebroids associated to Poisson actions, Duke Math. J. 86 (1997), 261-304.

55
Lu, J.-H. Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat Poisson structure on $G/B$, Transform. Groups 4 (1999).

56
Lu J.-H., Classical dynamical $r$-matrices and homogeneous Poisson structures on $G/H$ and $K/T$, Comm. Math. Phys. 212, 337-370 (2002).

57
Lu J.-H. e Weinstein A., Poisson-Lie groups, dressing transformations and Bruhat decompositions, J. Diff. Geom. 31, 501-526 (1990).

58
Michaelis W., Lie coalgebras, Adv. Math. 38, 1-54 (1980).

59
Michaelis W. A class of infinite-dimensional Lie bialgebras containing the Virasoro algebra, Adv. Math. 107, 365-392 (1994).

60
Montaldi J, Ortega J.-P. and Ratiu T, The relation between local and global dual pairs Math. Res. Lett. 11, 355-363 (2004).

61
Natsume and Olsen

62
Papadopoulo G., Homologies associées aux variétés de Poisson, Math. Ann. 318, 397-416 (2000).

63
G. B. Podkolzin and L. I. Vainerman, Quantum Stiefel manifolds and double cosets of quantum unitary group, Pac. J. Math. 138 (1999), 179-199.

64
D. Roytenberg, Poisson cohomology of $\SU(2)$-covariant "necklace" Poisson structures on ${\mathbb
S}^2$, Journ. Nonlin. Math. Phys. 9, 347-356 (2002).

65
Severa P. and Weinstein A., Poisson geometry with a 3-form background, Prog. Theo. Phys. Suppl. 144, 145-154 (2001).

66
A. J.-L. Sheu, Compact quantum groups and groupoid C*-algebras, J. Func. Anal. 144 (1997), 371-393.

67
A. J.-L. Sheu, Groupoid approach to quantum projective spaces, Contemp. Math. 228 (1998), 341-350.

68
A. J.-L. Sheu, Covariant Poisson structures on complex projective spaces, Comm. Anal. Geom. 10 (2002), 61-78.

69
J. Stokman, The quantum orbit method for generalized flag manifolds, Math. Res. Lett. 10 (2003), 469-481.

70
B. Tsygan, Formality conjecture for chains, in "Differential Topology, infinite-dimensional Lie algebras and applications" 261-274, Amer. Math. Soc. Transl. Ser. 2 194, AMS, Providence RI 1999.

71
Vaisman I., Lectures on the geometry of Poisson manifolds, Progr. Math. 118, Birkhaüser (1994).

72
Weinstein A., The local structure of Poisson manifolds, J. Diff. Geom. 18, 523-557 (1983).

73
Weinstein A., Symplectic groupoids, geometric quantization and irrational rotation algebras, in Symplectic geometry, groupoids and integrable systems, Séminaire Sud-Rhodaniene á Berkeley, Springer 1991.

74
Weinstein A., The modular automorphism group of a Poisson manifold, Journ. Geom. Phys. 23, 379-394 (1997).

75
Weinstein A. and Xu P., Extensions of symplectic groupoids and quantization, Journ. für Reine Angew. Math. 417, 159-189 (1991).

76
Van den Bergh, M. Noncommutative homology of some three-dimensional quantum spaces. $K$-Theory 8 (1994), 213-230.

77
Xu P., Morita equivalence of Poisson manifolds, Comm. Math. Phys., 142, 493-509 (1991).

78
Xu, Ping, Gerstenhaber algebras and BV-algebras in Poisson geometry, Comm. Math. Phys. 200 (1999), 545-560.

79
Xu P., Dirac submanifolds and Poisson involutions, Ann. Sci. École Norm. Sup. 36, 403-430 (2003).

80
V. Dolgushev, A formality theorem for chains, Adv. Math. at press.

81
Hawkins E., The structure of noncommutative deformations, math.QA/0504232.

82
Kosmann-Schwarzbach Y., Lie bialgebras, Poisson Lie groups and dressing transformations, preprint Centre de Mathématiques - Ecole Polytechnique, n. 22/1997.

DaSo
P. Dazord and D. Sondaz, Groupes de Poisson affines, in `Symplectic Geometry, Groupoids, and Integrable Systems', P. Dazord and A. Weinstein (Eds.), Springer-Verlag, 1991.

83
Stachura P., Double Lie algebras and Manin triple, preprint math.QA/9912???.

84
Zakrzewski S., Poisson structures on the Poincaré groups, Comm. Math. Phys,. ??????? Poisson structures on PoincarŽ group. Comm. Math. Phys. 185 (1997), no. 2, 285-311



Pawel Witkowski 2006-06-26