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Volumn 66, Issue 3, 2003, Pages 157-216

Deformation quantization of Poisson manifolds

Author keywords

Deformation quantization; Homotopy Lie algebras

Indexed keywords


EID: 3843152796     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MATH.0000027508.00421.bf     Document Type: Article
Times cited : (1604)

References (48)
  • 1
  • 2
    • 0036341597 scopus 로고    scopus 로고
    • Choix des signes pour la formalité de M. Kontsevich
    • Arnal, D., Manchon, D. and Masmoudi, M.: Choix des signes pour la formalité de M. Kontsevich. Pacific. J. Math. 203 (2002), 23-66.
    • (2002) Pacific. J. Math. , vol.203 , pp. 23-66
    • Arnal, D.1    Manchon, D.2    Masmoudi, M.3
  • 5
    • 85014454865 scopus 로고    scopus 로고
    • Frobenius manifolds and formality of Lie algebras of polyvector fields
    • Barannikov, S. and Kontsevich, M.: Frobenius manifolds and formality of Lie algebras of polyvector fields, Internat. Math. Res. Notices 1998(4) (1998), 201-215.
    • (1998) Internat. Math. Res. Notices , vol.1998 , Issue.4 , pp. 201-215
    • Barannikov, S.1    Kontsevich, M.2
  • 6
    • 33744769996 scopus 로고
    • Deformation theory and quantization. I. Deformations of symplectic structures
    • Bayen, F., Flato, M., Frønsdal, C., Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization. I. Deformations of symplectic structures, Ann. Phys. 111(1) (1978), 61-110.
    • (1978) Ann. Phys. , vol.111 , Issue.1 , pp. 61-110
    • Bayen, F.1    Flato, M.2    Frønsdal, C.3    Lichnerowicz, A.4    Sternheimer, D.5
  • 8
    • 0001692169 scopus 로고    scopus 로고
    • On the AKSZ formulation of the Poisson sigma model
    • Cattaneo, A. and Felder, G.: On the AKSZ formulation of the Poisson sigma model, Lett. Math. Phys. 56(2) (2001), 163-179.
    • (2001) Lett. Math. Phys. , vol.56 , Issue.2 , pp. 163-179
    • Cattaneo, A.1    Felder, G.2
  • 9
    • 0034349089 scopus 로고    scopus 로고
    • A path integral approach to the Kontsevich quantization formula
    • Cattaneo, A. and Felder, G.: A path integral approach to the Kontsevich quantization formula, Comm. Math. Phys. 212(3) (2000), 591-611.
    • (2000) Comm. Math. Phys. , vol.212 , Issue.3 , pp. 591-611
    • Cattaneo, A.1    Felder, G.2
  • 10
    • 0036872347 scopus 로고    scopus 로고
    • From local to global deformation quantization of Poisson manifolds
    • Cattaneo, A., Felder, G. and Tomassini, L.: From local to global deformation quantization of Poisson manifolds, Duke Math. J. 115(2) (2002), 329-352.
    • (2002) Duke Math. J. , vol.115 , Issue.2 , pp. 329-352
    • Cattaneo, A.1    Felder, G.2    Tomassini, L.3
  • 12
    • 0000898844 scopus 로고
    • Existence of star-products and of formal deformations in Poisson Lie algebra of arbitrary symplectic manifolds
    • De Wilde, M. and Lecomte, P.B.A.: Existence of star-products and of formal deformations in Poisson Lie algebra of arbitrary symplectic manifolds, Lett. Math. Phys. 7 (1983), 487-496.
    • (1983) Lett. Math. Phys. , vol.7 , pp. 487-496
    • De Wilde, M.1    Lecomte, P.B.A.2
  • 13
    • 0009804827 scopus 로고
    • Caractères des algèbres de Lie résolubles
    • Duflo, M.: Caractères des algèbres de Lie résolubles, C.R. Acad. Sci. Sér. A 269 (1969), 437-438.
    • (1969) C.R. Acad. Sci. Sér. A , vol.269 , pp. 437-438
    • Duflo, M.1
  • 14
    • 0007149170 scopus 로고    scopus 로고
    • Quantization of lie bialgebras, I
    • Etingof, P. and Kazhdan, D.: Quantization of Lie Bialgebras, I, Selecta Math. (New Ser.) 2(1) (1996), 1-41.
    • (1996) Selecta Math. (New Ser.) , vol.2 , Issue.1 , pp. 1-41
    • Etingof, P.1    Kazhdan, D.2
  • 15
    • 84972506966 scopus 로고
    • A simple geometric construction of deformation quantization
    • Fedosov, B.: A simple geometric construction of deformation quantization, J. Differential Geom. 40(2) (1994), 213-238.
    • (1994) J. Differential Geom. , vol.40 , Issue.2 , pp. 213-238
    • Fedosov, B.1
  • 16
    • 0002028905 scopus 로고    scopus 로고
    • Deformation quantization with traces
    • Felder, G. and Shoikhet, B.: Deformation quantization with traces, Lett. Math. Phys. 53 (1) (2000), 75-86.
    • (2000) Lett. Math. Phys. , vol.53 , Issue.1 , pp. 75-86
    • Felder, G.1    Shoikhet, B.2
  • 17
    • 0000688160 scopus 로고
    • Compactification of configuration spaces
    • Fulton, W. and MacPherson, R.: Compactification of configuration spaces, Ann. of Math. (2) 139(1) (1994), 183-225.
    • (1994) Ann. of Math. (2) , vol.139 , Issue.1 , pp. 183-225
    • Fulton, W.1    MacPherson, R.2
  • 18
    • 0000825912 scopus 로고
    • Some problems of differential geometry and the calculation of cohomologies of Lie algebras of vector fields
    • Gelfand, I. M. and Kazhdan D. A.: Some problems of differential geometry and the calculation of cohomologies of Lie algebras of vector fields, Soviet Math. Dokl. 12(5) (1971), 1367-1370.
    • (1971) Soviet Math. Dokl. , vol.12 , Issue.5 , pp. 1367-1370
    • Gelfand, I.M.1    Kazhdan, D.A.2
  • 19
    • 0001467148 scopus 로고
    • Homotopy G-algebras and moduli space operad
    • Gerstenhaber, M. and Voronov, A.: Homotopy G-algebras and moduli space operad, Internat. Math. Res. Notices 1995(3) (1995), 141-153.
    • (1995) Internat. Math. Res. Notices , vol.1995 , Issue.3 , pp. 141-153
    • Gerstenhaber, M.1    Voronov, A.2
  • 21
    • 0010536648 scopus 로고
    • Method of orbits in the representation theory of complex Lie groups
    • Ginzburg, V.: Method of orbits in the representation theory of complex Lie groups, Funct. Anal. Appl. 15(1) (1981), 18-28.
    • (1981) Funct. Anal. Appl. , vol.15 , Issue.1 , pp. 18-28
    • Ginzburg, V.1
  • 22
    • 84972565878 scopus 로고
    • The homotopy invariance of the Kuranishi space, Illinois
    • Goldman, W. and Millson, J.: The homotopy invariance of the Kuranishi space, Illinois. J. Math. 34(2) (1990), 337-367.
    • (1990) J. Math. , vol.34 , Issue.2 , pp. 337-367
    • Goldman, W.1    Millson, J.2
  • 23
    • 0038515377 scopus 로고    scopus 로고
    • Tamarkin's proof of Kontsevich formality theorem
    • Hinich, V.: Tamarkin's proof of Kontsevich formality theorem, Forum Math. 15(4) (2003), 591-614.
    • (2003) Forum Math. , vol.15 , Issue.4 , pp. 591-614
    • Hinich, V.1
  • 24
    • 0042725382 scopus 로고    scopus 로고
    • Deformation theory and Lie algebra homology, I. II
    • Hinich, V. and Schechtman, V.: Deformation theory and Lie algebra homology, I. II., Algebra Colloq. 4(2) (1997), 213-240, and 4(3) (1997), 291-316.
    • (1997) Algebra Colloq. , vol.4 , Issue.2 , pp. 213-240
    • Hinich, V.1    Schechtman, V.2
  • 25
    • 0040513616 scopus 로고    scopus 로고
    • Hinich, V. and Schechtman, V.: Deformation theory and Lie algebra homology, I. II., Algebra Colloq. 4(2) (1997), 213-240, and 4(3) (1997), 291-316.
    • (1997) Algebra Colloq. , vol.4 , Issue.3 , pp. 291-316
  • 26
    • 0002039359 scopus 로고
    • Homotopy Lie algebras
    • Adv. Soviet Math., Amer. Math. Soc., Providence, RI
    • Hinich, V. and Schechtman, V.: Homotopy Lie algebras, In: I. M. Gelfand Seminar, Adv. Soviet Math. 16(2), Amer. Math. Soc., Providence, RI, 1993, pp. 1-28.
    • (1993) I. M. Gelfand Seminar , vol.16 , Issue.2 , pp. 1-28
    • Hinich, V.1    Schechtman, V.2
  • 29
    • 0000887706 scopus 로고
    • The Campbell-Hausdorff formula and invariant hyperfunctions
    • Kashiwara, M. and Vergne, M.: The Campbell-Hausdorff formula and invariant hyperfunctions, Invent. Math. 47 (1978), 249-272.
    • (1978) Invent. Math. , vol.47 , pp. 249-272
    • Kashiwara, M.1    Vergne, M.2
  • 31
    • 0001499677 scopus 로고
    • Feynman diagrams and low-dimensional topology
    • Progr. in Math. 120, Birkhäuser, Basel
    • Kontsevich, M.: Feynman diagrams and low-dimensional topology, In: First European Congress of Mathematics (Paris, 1992), Vol. II, Progr. in Math. 120, Birkhäuser, Basel, 1994, pp. 97-121.
    • (1994) First European Congress of Mathematics (Paris 1992), Vol. II , vol.2 , pp. 97-121
    • Kontsevich, M.1
  • 32
    • 0002342806 scopus 로고    scopus 로고
    • Formality conjecture
    • D. Sternheimer et al. (eds), Kluwer, Dordrecht
    • Kontsevich, M.: Formality conjecture, In: D. Sternheimer et al. (eds), Deformation Theory and Symplectic Geometry, Kluwer, Dordrecht, 1997, pp. 139-156.
    • (1997) Deformation Theory and Symplectic Geometry , pp. 139-156
    • Kontsevich, M.1
  • 33
    • 0042786153 scopus 로고    scopus 로고
    • Rozansky-Witten invariants via formal geometry
    • Kontsevich, M.: Rozansky-Witten invariants via formal geometry, Compositio Math. 115(1) (1999), 115-127.
    • (1999) Compositio Math. , vol.115 , Issue.1 , pp. 115-127
    • Kontsevich, M.1
  • 34
    • 0000302037 scopus 로고
    • Homological algebra of mirror symmetry
    • Birkhäuser, Basel
    • Kontsevich, M.: Homological algebra of mirror symmetry, In: Proceedings of ICM, (Zürich 1994) Vol. I, Birkhäuser, Basel, 1995, pp. 120-139.
    • (1995) Proceedings of ICM, (Zürich 1994) Vol. I , vol.1 , pp. 120-139
    • Kontsevich, M.1
  • 36
    • 0003193329 scopus 로고    scopus 로고
    • Operads and motives in deformation quantization
    • Kontsevich, M.: Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1) (1999), 35-72.
    • (1999) Lett. Math. Phys. , vol.48 , Issue.1 , pp. 35-72
    • Kontsevich, M.1
  • 37
    • 0042704087 scopus 로고    scopus 로고
    • Deformation quantization of algebaric varieties
    • Kontsevich, M.: Deformation quantization of algebaric varieties, Lett. Math. Phys. 56(3) (2001), 271-294.
    • (2001) Lett. Math. Phys. , vol.56 , Issue.3 , pp. 271-294
    • Kontsevich, M.1
  • 38
    • 0008028610 scopus 로고    scopus 로고
    • Deformations of algebras over operads and the Deligne conjecture
    • G. Dito and D. Sternheimer (eds), Kluwer Acad. Publ., Dordrecht
    • Kontsevich, M. and Soibelman, Y.: Deformations of algebras over operads and the Deligne conjecture, In: G. Dito and D. Sternheimer (eds), Conférence Moshé Flato 1999, Vol. I (Dijon 1999), Kluwer Acad. Publ., Dordrecht, 2000, pp. 255-307.
    • (2000) Conférence Moshé Flato 1999, Vol. I (Dijon 1999) , vol.1 , pp. 255-307
    • Kontsevich, M.1    Soibelman, Y.2
  • 39
    • 0038052509 scopus 로고    scopus 로고
    • A solution of Deligne's Hochschild cohomology conjecture
    • Contemp. Math. 293, Amer. Math. Soc., Providence, RI
    • McClure, M. and Smith, J.: A solution of Deligne's Hochschild cohomology conjecture, In: Recent Progress in Homotopy Theory (Baltimore, MD, 2000), Contemp. Math. 293, Amer. Math. Soc., Providence, RI, 2002, pp. 153-193.
    • (2002) Recent Progress in Homotopy Theory (Baltimore, MD, 2000) , pp. 153-193
    • McClure, M.1    Smith, J.2
  • 42
    • 0040185353 scopus 로고
    • Superconnections and the Chern character
    • Quillen, D.: Superconnections and the Chern character, Topology 24 (1985), 89-95.
    • (1985) Topology , vol.24 , pp. 89-95
    • Quillen, D.1
  • 43
    • 0001164659 scopus 로고
    • The Lie algebra structure on tangent cohomology and deformation theory
    • Schlessinger, M. and Stasheff, J.: The Lie algebra structure on tangent cohomology and deformation theory, J. Pure Appl. Algebra 38 (1985), 313-322.
    • (1985) J. Pure Appl. Algebra , vol.38 , pp. 313-322
    • Schlessinger, M.1    Stasheff, J.2
  • 44
    • 51649170201 scopus 로고
    • Infinitesimal computations in topology
    • 1977
    • Sullivan, D.: Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977) No. 47, (1978), 269-331.
    • (1978) Inst. Hautes Études Sci. Publ. Math. , vol.47 , pp. 269-331
    • Sullivan, D.1
  • 45
    • 0009491437 scopus 로고    scopus 로고
    • Quantizing poisson manifolds
    • Contemp. Math. 214, Amer. Math. Soc., Providence, RI
    • Voronov, A.: Quantizing Poisson manifolds, In: Perspectives on Quantization (South Hadley, MA, 1996), Contemp. Math. 214, Amer. Math. Soc., Providence, RI, 1998, pp. 189-195.
    • (1998) Perspectives on Quantization (South Hadley, MA, 1996) , pp. 189-195
    • Voronov, A.1
  • 47
    • 3843129069 scopus 로고    scopus 로고
    • Quantization of Lie bialgebras via the formality of the operad of little disks
    • G.Halbout (ed.), IRMA Lectures in Math. Theoret. Phys. Walter de Gruyter, Berlin
    • Tamarkin, D.: Quantization of Lie bialgebras via the formality of the operad of little disks, in: G.Halbout (ed.), Deformation Quantization (Strasbourg 2001), IRMA Lectures in Math. Theoret. Phys. Vol. I, Walter de Gruyter, Berlin, 2002, pp. 203-236.
    • (2002) Deformation Quantization (Strasbourg 2001) , vol.1 , pp. 203-236
    • Tamarkin, D.1
  • 48
    • 0042189964 scopus 로고    scopus 로고
    • Noncommutative differential calculus, homotopy BV algebras and formality conjectures
    • Tamarkin, D. and Tsygan, B.: Noncommutative differential calculus, homotopy BV algebras and formality conjectures, Methods Funct. Anal. Topology 6(2) (2000), 85-100.
    • (2000) Methods Funct. Anal. Topology , vol.6 , Issue.2 , pp. 85-100
    • Tamarkin, D.1    Tsygan, B.2


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