On the fedosov deformation quantization beyond the regular poisson manifolds

Nuclear Physics B

Volumn 645, Issue 3, 2002, Pages 457-476

  Dolgushev, V A ^a   Isaev, A P ^a   Lyakhovich, S L ^a   Sharapov, A A ^a  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

Deformation quantization; Quantum groups

Indexed keywords

EID: 0037175457     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(02)00763-0     Document Type: Article

References (31)

1. F.A. Berezin, Izv. Akad. Nauk 38 (1974) 1116;
2. F.A. Berezin, Commun. Math. Phys. 40 (1975) 153.
3. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, Ann. Phys. (N.Y.) 110 (1978) 111;
4. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, Ann. Phys. (N.Y.) 111 (1978) 61.
5. D. Sternheimer, Deformation quantization: Twenty years after, math/9809056.
6. M. Kontsevich, Deformation quantization of Poisson manifolds, q-alg/9709040.
7. B.V. Fedosov, J. Differential Geom. 40 (1994) 213.
8. B.V. Fedosov, Deformation Quantization and Index Theory, Mathematical Topics, Vol. 9, Akademie Verlag, Berlin, 1996.
9. d, Memoirs AMS, Vol. 506, American Mathematical Society, Providence, 1993.
10. M.A. Rieffel, Contemp. Math. 228 (1998) 315-326, quant-ph/9712009.
11. V. Drinfeld, Sov. Math. Dokl. 28 (1983) 667-671.
12. A.G. Elashvili, Funct. Anal. Appl. 16 (1982) 94-95.
13. D. Ananikian, P.P. Kulish, V.D. Lyakhovsky, Full chains of twists for symplectic algebras, math.QA/0109083.
14. P.P. Kulish, V.D. Lyakhovsky, A. Stolin, math.QA/0010147.
15. P.P. Kulish, V.D. Lyakhovsky, M.A. del Olmo, J. Phys. A 32 (1999) 8671, math.QA/9908061.
16. M. Bordemann, St. Waldmann, Lett. Math. Phys. 41 (1997) 243-253, q-alg/9605012.
17. M.A. Grigoriev, S.L. Lyakhovich, Commun. Math. Phys. 218 (2001) 437, hep-th/0003114.
18. I.A. Batalin, M.A. Grigoriev, S.L. Lyakhovich, Theor. Math. Phys. 128 (2001) 1109-1139, hep-th/0101089.
19. V.A. Dolgushev, S.L. Lyakhovich, A.A. Sharapov, Nucl. Phys. B 606 (2001) 647-672, hep-th/0101032.
20. A.V. Karabegov, M. Schlichenmaier, math.QA/0102169, Mannheimer Manuskripte 260.
21. A.S. Cattaneo, G. Felder, L. Tomassini, From local to global deformation quantization of Poisson manifolds, math.QA/0012228.
22. L.A. Takhtajan, Lectures on Quantum Groups, in: Nankai Lectures Notes Math. Phys., 1990, pp. 69-197.
23. A. Giaquinto, J. Zhang, Bialgebra action, twists, and universal deformation formula, hep-th/9411140.
24. P. Xu, Triangular dynamical r-matrices and quantization, math.QA/0005006.
25. I. Vaisman, Fedosov quantization on symplectic ringed spaces, math.SG/0106070.
26. M.V. Karasev, V.P. Maslov, Nonlinear Poisson Brackets: Geometry and Quantization, American Mathematical Society, Providence, 1993.
27. A.S. Cattaneo, G. Felder, A path integral approach to the Kontsevich quantization formular, q-alg/9902090.
28. V. Coll, M. Gerstenhaber, A. Giaquinto, in: Israel Math. Conference Proceedings Ring Theory, Vol. 1, Weizmann Sci. Press, New York, 1989, pp. 396-403.
29. L.D. Faddeev, N.Yu. Reshetikhin, L.A. Takhtajan, Algebra Anal. 1 (1989) 178-206.
30. I.A. Batalin, I.V. Tyutin, Int. J. Mod. Phys. A 6 (1991) 3255.
31. S.L. Lyakhovich, A.A. Sharapov, in preparation.