Covariant and equivariant formality theorems

Advances in Mathematics

Volumn 191, Issue 1, 2005, Pages 147-177

  Dolgushev, Vasiliy ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Deformation quantization; Formality theorems

Indexed keywords

EID: 6444231699     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aim.2004.02.001     Document Type: Article

References (21)

1. Alekseev A. Meinrenken E. The non-commutative Weil algebra Invent. Math. 139 1 2000 135-172 math.DG/9903052
2. Baulieu L. Losev A. Nekrasov N. Target space symmetries in topological theories I J. High Energy Phys. 0202 2002 021
3. A.S. Cattaneo, G. Felder, On the globalization of Kontsevich's star product and the perturbative Poisson sigma model, hep-th/0111028.
4. Cattaneo A.S. Felder G. Tomassini L. From local to global deformation quantization of Poisson manifolds Duke Math. J. 115 2 2002 329-352 math.QA/0012228
5. Dolgushev V.A. Isaev A.P. Lyakhovich S.L. Sharapov A.A. On the Fedosov deformation quantization beyond the regular Poisson manifolds Nucl. Phys. B 645 3 2002 457-476
6. C. Emmrich, A. Weinstein, The differential geometry of Fedosov's quantization, Lie theory and geometry, Progr. Math., Vol. 123, Birkhauser, Boston, MA, 1994, 217-239; hep-th/9311094.
7. B. Enriquez, P. Etingof, Quantization of Alekseev-Meinrenken dynamical r-matrices, math.QA/0302067.
8. B. Enriquez, P. Etingof, Quantization of classical dynamical r-matrices with non-abelian base, math. QA/0311224.
9. Etingof P. Nikshych D. Vertex-IRF transformations and quantization of dynamical r-matrices Math. Res. Lett. 8 3 2001 331-346
10. Etingof P. Varchenko A. Geometry and classification of solutions of the classical dynamical Yang-Baxter equation Comm. Math. Phys. 192 1 1998 77-120
11. Fedosov B.V. A simple geometrical construction of deformation quantization J. Differential Geom. 40 1994 213-238
12. Gelfand I. Retakh V. Shubin M. Fedosov manifolds Adv. Math. 136 1 1998 104-140 dg-ga/9707024
13. Hasegawa K. L-operator for Belavin's R-matrix acting on the space of theta functions J. Math. Phys. 35 1994 6158-6171
14. Hinich V. Schechtman V. Homotopy Lie algebras, I.M. Gelfand Seminar Adv. Sov. Math. 16 2 1993 1-28
15. M. Kontsevich, Deformation quantization of Poisson manifolds, I, q-alg/9709040.
16. Kontsevich M. Deformation quantization of algebraic varieties Lett. Math. Phys. 56 3 2001 271-294 math.QA/0106006
17. T. Mochizuki, An application of formality theorem to a quantization of dynamical r-matrices, http://www.math.ias.edu/takuro/dyb.ps
18. Quillen D. Rational homotopy theory Ann. Math. 90 2 1969 205-295
19. D. Tamarkin, Another proof of M. Kontsevich formality theorem, math.QA/9803025.
20. Xu P. Triangular dynamical r-matrices and quantization Adv. Math. 166 1 2002 1-49 math.QA/0005006
21. Xu P. Quantum dynamical Yang-Baxter equation over a nonabelian base Comm. Math. Phys. 226 3 2002 475-495 math.QA/0104071