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Fresse, Benoit
Théorie des opérades de Koszul et homologie des algèbres de Poisson. Annales mathématiques Blaise Pascal, 13 no. 2 (2006), p. 237-312
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[1] J. Alev and T. Lambre, Comparaison de l’homologie de Hochschild et de l’homologie de Poisson pour une déformation des surfaces de Klein, Algebra and operator theory, Kluwer Acad. Publ., pages 25-38, 1998 MR 1643407 | Zbl 0931.16007
[2] D. Balavoine, Homology and cohomology with coefficicients of an algebra over a quadratic operad, J. Pure Appl. Algebra, 132:221-258, 1998 MR 1642086 | Zbl 0967.18004
[3] C. Berger and I. Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv., 78:805-831, 2003 MR 2016697 | Zbl 1041.18011
[4] J. Braconnier, Algèbres de Poisson, C. R. Acad. Sci. Paris Sér. A Math., 284:1345-1348, 1977 MR 443000 | Zbl 0356.17007
[5] J.-L. Brylinski, A differential complex for Poisson manifolds, J. Diff. Geometry., 28:93-114, 1988 MR 950556 | Zbl 0634.58029
[6] D. Burghelea and M. Vigué-Poirrier, Cyclic homology of commutative algebras, Springer-Verlag, 1988 MR 952571 | Zbl 0666.13007
[7] K. T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. Math., 65:163-178, 1957 MR 85251 | Zbl 0077.25301
[8] K. T. Chen, Iterated path integral, Bull. Amer. Math. Soc., 83:831-879, 1977
Article | MR 454968 | Zbl 0389.58001
[9] V. G. Drinfeld, Quantum groups, Proc. Int. Congr. Math., pages 798-820, 1987 MR 934283 | Zbl 0667.16003
[10] V. G. Drinfeld, On some unsolved problems in quantum group theory, Quantum groups, Lecture Notes in Math., 1510, Springer-Verlag, pages 1-8, 1992 MR 1183474 | Zbl 0765.17014
[11] T. Fox and M. Markl, Distributive laws, bialgebras, and cohomology, Operads: Proceedings of renaissance conferences, Contemp. Math., 202, pages 167-205, 1997 MR 1436921 | Zbl 0866.18008
[12] B. Fresse, Algèbre des descentes et cogroupes dans les algèbres sur une opérade, Bull. Soc. Math. Fr., 126:407-433, 1998
Numdam | MR 1682797 | Zbl 0940.18004
[13] B. Fresse, Homologie de Quillen pour les algèbres de Poisson, C. R. Acad. Sci. Paris Sér. I Math., 326:1053-1058, 1998 MR 1647186 | Zbl 0922.17014
[14] B. Fresse, Structures de Poisson sur une intersection complète à singularitées isolées, C. R. Acad. Sci. Paris Sér. I Math., 335:5-10, 2002 MR 1920425 | Zbl 01777355
[15] B. Fresse, Koszul duality of operads and homology of partition posets, Homotopy theory and its applications, Contemp. Math., 346, pages 115-215, 2004 MR 2066499 | Zbl 1077.18007
[16] I. M. Gelfand and I. Y. Dorfman, Hamiltonian operators and the classical Yang-Baxter equation, Funkts. Anal. Prilozh., 16:1-9, 1982 MR 684122 | Zbl 0527.58018
[17] M. Gerstenhaber and S. D. Schack, A Hodge-type decomposition for commutative algebra cohomology, J. Pure Appl. Algebra, 48:229-247, 1987 MR 917209 | Zbl 0671.13007
[18] M. Gerstenhaber and S. D. Schack, The shuffle bialgebra and the cohomology of commutative algebras, J. Pure Appl. Algebra, 70:263-272, 1991 MR 1104844 | Zbl 0728.13003
[19] E. Getzler and J. Jones, Operads, homotopy algebra and iterated integrals for double loop spaces, prépublication arXiv:hep-th/9403055, 1994
arXiv
[20] G. Ginot, Homologie et modèle minimal des algèbres de Gerstenhaber, Ann. Math. Blaise Pascal, 11:95-127, 2004
Numdam | MR 2077240 | Zbl 02207860
[21] V. Ginzburg and D. Kaledin, Poisson deformations of symplectic quotient singularities, Adv. Math., 186:1-57, 2004 MR 2065506 | Zbl 1062.53074
[22] V. Ginzburg and M. Kapranov, Koszul duality for operads, Duke Math. J., 76:203-272, 1995
Article | MR 1301191 | Zbl 0855.18006
[23] R. Hain, On the indecomposable elements of the bar construction, Proc. Amer. Math. Soc., 98:312-316, 1986 MR 854039 | Zbl 0613.55007
[24] J. Huebschmann, Poisson cohomology and quantization, J. Reine Angew. Math., 408:57-113, 1990 MR 1058984 | Zbl 0699.53037
[25] C. Kassel, L’homologie cyclique des algèbres enveloppantes, Invent. Math., 91:221-251, 1988 MR 922799 | Zbl 0653.17007
[26] M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys., 66:157-216, 2003 MR 2062626 | Zbl 1058.53065
[27] J.-L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, Elie Cartan et les mathématiques d’aujourd’hui, Astérisque hors série, pages 257-271, 1985 MR 837203 | Zbl 0615.58029
[28] I. S. Krasilshschik, Hamiltonian cohomology of canonical algebras, Dokl. Akad. Nauk., 251:1306-1309, 1980 MR 570152 | Zbl 0454.58020
[29] A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geometry, 12:253-300, 1977 MR 501133 | Zbl 0405.53024
[30] M. Livernet, Homotopie rationnelle des algèbres sur une opérade, Ph. D. Thesis, Université Louis Pasteur, 1998 MR 1695322
[31] J.-L. Loday, Opérations sur l’homologie cyclique des algèbres commutatives, Invent. Math., 96:205-230, 1989 MR 981743 | Zbl 0686.18006
[32] J.-L. Loday, Cyclic homology, Grund. der Math. Wiss. 301, Springer-Verlag, 1992 MR 1217970 | Zbl 0780.18009
[33] J.-L. Loday, Série de Hausdorff, idempotents Euleriens et algèbres de Hopf, Exposition. Math., 12:165-178, 1994 MR 1274784 | Zbl 0807.17003
[34] S. Mac Lane, Homology, Grund. der Math. Wiss. 114, Springer-Verlag, 1963 MR 1344215
[35] M. Markl, Distributive laws and Koszulness, Ann. Inst. Fourier, 46:307-323, 1996
Numdam | MR 1393517 | Zbl 0853.18005
[36] M. Markl, S. Shnider and J. Stasheff, Operads in algebra, topology and physics, Mathematical Surveys and Monographs 96, American Mathematical Society, 2002 MR 1898414 | Zbl 1017.18001
[37] S.-Q. Oh, Poisson enveloping algebras, Comm. Algebra, 27:2181-2186, 1999 MR 1683858 | Zbl 0936.16020
[38] F. Patras, Construction géométrique des idempotents Euleriens. Filtration des groupes de polytopes et des groupes d’homologie de Hochschild, Bull. Soc. Math. Fr., 119:173-198, 1991
Numdam | MR 1116844 | Zbl 0752.55014
[39] F. Patras, L’algèbre des descentes d’une bigèbre graduée, J. Algebra, 170:547-566, 1994 MR 1302855 | Zbl 0819.16033
[40] T. Pirashvili, Hodge decomposition for higher Hochschild homology, Ann. Sci. École Norm. Sup., 33:151-179, 2000
Numdam | MR 1755114 | Zbl 0957.18004
[41] D. Quillen, Homotopical algebra, Lecture Notes in Math. 43, Springer-Verlag, 1967 MR 223432 | Zbl 0168.20903
[42] D. Quillen, Rational homotopy theory, Ann. of Math., 90:205-295, 1969 MR 258031 | Zbl 0191.53702
[43] D. Quillen, On the (co)-homology of commutative rings, Amer. Math. Soc., 1970 MR 257068 | Zbl 0234.18010
[44] C. Reutenauer, Theorem of Poincaré-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to Stirling numbers, Combinatoire énumérative, Lecture Notes in Math., 1234, Springer-Verlag, pages 267-284, 1986 MR 927769 | Zbl 0621.20004
[45] C. Reutenauer, Free Lie Algebras, London Math. Soc. Mon. 7, Clarendon Press, 1993 MR 1231799 | Zbl 0798.17001
[46] G. Rinehart, Differential forms on general commutative algebras, Trans. Amer. Math. Soc., 108:195-222, 1963 MR 154906 | Zbl 0113.26204
[47] M. Schlessinger and J. Stasheff, The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra, 38:313-322, 1985 MR 814187 | Zbl 0576.17008
[48] D. Tamarkin, Another proof of M. Kontsevich formality theorem, prépublication arXiv:math.QA/9803025, 1998
arXiv
[49] I. Vaisman, Lectures on the geometry of Poisson manifolds, Progress in Math. 118, Birkhäuser, 1994 MR 1269545 | Zbl 0810.53019
[50] M. Vigué-Poirrier, Cyclic homology of algebraic hypersurfaces, J. Pure Appl. Algebra, 72:95-108, 1991 MR 1115570 | Zbl 0732.16008
[51] M. Vigué-Poirrier, Décompositions de l’homologie cyclique des algèbres différentielles graduées commutatives, K-theory, 4:255-267, 1991 MR 1116926
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