Théorie des opérades de Koszul et homologie des algèbres de Poisson
Fresse, Benoit
Annales mathématiques Blaise Pascal, Tome 13 (2006), p. 237-312 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AMBP_2006__13_2_237_0,
     author = {Fresse, Benoit},
     title = {Th\'eorie des op\'erades de Koszul et homologie des alg\`ebres de Poisson},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {13},
     year = {2006},
     pages = {237-312},
     doi = {10.5802/ambp.219},
     zbl = {1141.55006},
     mrnumber = {2275449},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AMBP_2006__13_2_237_0}
}

Fresse, Benoit. Théorie des opérades de Koszul et homologie des algèbres de Poisson. Annales mathématiques Blaise Pascal, Tome 13 (2006) pp. 237-312. doi : 10.5802/ambp.219. http://gdmltest.u-ga.fr/item/AMBP_2006__13_2_237_0/

[1] Alev, J.; Lambre, T. 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. (1998), pp. 25-38 | MR 1643407 | Zbl 0931.16007

[2] Balavoine, D. Homology and cohomology with coefficicients of an algebra over a quadratic operad, J. Pure Appl. Algebra, Tome 132 (1998), pp. 221-258 | Article | MR 1642086 | Zbl 0967.18004

[3] Berger, C.; Moerdijk, I. Axiomatic homotopy theory for operads, Comment. Math. Helv., Tome 78 (2003), pp. 805-831 | Article | MR 2016697 | Zbl 1041.18011

[4] Braconnier, J. Algèbres de Poisson, C. R. Acad. Sci. Paris Sér. A Math., Tome 284 (1977), pp. 1345-1348 | MR 443000 | Zbl 0356.17007

[5] Brylinski, J.-L. A differential complex for Poisson manifolds, J. Diff. Geometry., Tome 28 (1988), pp. 93-114 | MR 950556 | Zbl 0634.58029

[6] Burghelea, D.; Vigué-Poirrier, M. Cyclic homology of commutative algebras, Springer-Verlag, Lecture Notes in Math., Tome 1318 (1988), pp. 51-72 | MR 952571 | Zbl 0666.13007

[7] Chen, K. T. Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. Math., Tome 65 (1957), pp. 163-178 | Article | MR 85251 | Zbl 0077.25301

[8] Chen, K. T. Iterated path integral, Bull. Amer. Math. Soc., Tome 83 (1977), pp. 831-879 | Article | MR 454968 | Zbl 0389.58001

[9] Drinfeld, V. G. Quantum groups, Proc. Int. Congr. Math. (1987), pp. 798-820 | MR 934283 | Zbl 0667.16003

[10] Drinfeld, V. G. On some unsolved problems in quantum group theory, Quantum groups, Springer-Verlag (Lecture Notes in Math.) Tome 1510 (1992), pp. 1-8 | MR 1183474 | Zbl 0765.17014

[11] Fox, T.; Markl, M. Distributive laws, bialgebras, and cohomology, Operads : Proceedings of renaissance conferences (Contemp. Math.) Tome 202 (1997), pp. 167-205 | MR 1436921 | Zbl 0866.18008

[12] Fresse, B. Algèbre des descentes et cogroupes dans les algèbres sur une opérade, Bull. Soc. Math. Fr., Tome 126 (1998), pp. 407-433 | Numdam | MR 1682797 | Zbl 0940.18004

[13] Fresse, B. Homologie de Quillen pour les algèbres de Poisson, C. R. Acad. Sci. Paris Sér. I Math., Tome 326 (1998), pp. 1053-1058 | Article | MR 1647186 | Zbl 0922.17014

[14] Fresse, B. Structures de Poisson sur une intersection complète à singularitées isolées, C. R. Acad. Sci. Paris Sér. I Math., Tome 335 (2002), pp. 5-10 | MR 1920425 | Zbl 01777355

[15] Fresse, B. Koszul duality of operads and homology of partition posets, Homotopy theory and its applications (Contemp. Math.) Tome 346 (2004), pp. 115-215 | MR 2066499 | Zbl 1077.18007

[16] Gelfand, I. M.; Dorfman, I. Y. Hamiltonian operators and the classical Yang-Baxter equation, Funkts. Anal. Prilozh., Tome 16 (1982), pp. 1-9 | MR 684122 | Zbl 0527.58018

[17] Gerstenhaber, M.; Schack, S. D. A Hodge-type decomposition for commutative algebra cohomology, J. Pure Appl. Algebra, Tome 48 (1987), pp. 229-247 | Article | MR 917209 | Zbl 0671.13007

[18] Gerstenhaber, M.; Schack, S. D. The shuffle bialgebra and the cohomology of commutative algebras, J. Pure Appl. Algebra, Tome 70 (1991), pp. 263-272 | Article | MR 1104844 | Zbl 0728.13003

[19] Getzler, E.; Jones, J. Operads, homotopy algebra and iterated integrals for double loop spaces (1994) (prépublication arXiv :hep-th/9403055)

[20] Ginot, G. Homologie et modèle minimal des algèbres de Gerstenhaber, Ann. Math. Blaise Pascal, Tome 11 (2004), pp. 95-127 | Article | Numdam | MR 2077240 | Zbl 02207860

[21] Ginzburg, V.; Kaledin, D. Poisson deformations of symplectic quotient singularities, Adv. Math., Tome 186 (2004), pp. 1-57 | Article | MR 2065506 | Zbl 1062.53074

[22] Ginzburg, V.; Kapranov, M. Koszul duality for operads, Duke Math. J., Tome 76 (1995), pp. 203-272 | Article | MR 1301191 | Zbl 0855.18006

[23] Hain, R. On the indecomposable elements of the bar construction, Proc. Amer. Math. Soc., Tome 98 (1986), pp. 312-316 | Article | MR 854039 | Zbl 0613.55007

[24] Huebschmann, J. Poisson cohomology and quantization, J. Reine Angew. Math., Tome 408 (1990), pp. 57-113 | Article | MR 1058984 | Zbl 0699.53037

[25] Kassel, C. L’homologie cyclique des algèbres enveloppantes, Invent. Math., Tome 91 (1988), pp. 221-251 | Article | MR 922799 | Zbl 0653.17007

[26] Kontsevich, M. Deformation quantization of Poisson manifolds, Lett. Math. Phys., Tome 66 (2003), pp. 157-216 | Article | MR 2062626 | Zbl 1058.53065

[27] Koszul, J.-L. Crochet de Schouten-Nijenhuis et cohomologie, Elie Cartan et les mathématiques d’aujourd’hui (Astérisque hors série) (1985), pp. 257-271 | MR 837203 | Zbl 0615.58029

[28] Krasilshschik, I. S. Hamiltonian cohomology of canonical algebras, Dokl. Akad. Nauk., Tome 251 (1980), pp. 1306-1309 | MR 570152 | Zbl 0454.58020

[29] Lichnerowicz, A. Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geometry, Tome 12 (1977), pp. 253-300 | MR 501133 | Zbl 0405.53024

[30] Livernet, M. Homotopie rationnelle des algèbres sur une opérade, Strasbourg, Université Louis Pasteur (1998) (Ph. D. Thesis) | MR 1695322

[31] Loday, J.-L. Opérations sur l’homologie cyclique des algèbres commutatives, Invent. Math., Tome 96 (1989), pp. 205-230 | Article | MR 981743 | Zbl 0686.18006

[32] Loday, J.-L. Cyclic homology, Springer-Verlag, Grund. der Math. Wiss., Tome 301 (1992) | MR 1217970 | Zbl 0780.18009

[33] Loday, J.-L. Série de Hausdorff, idempotents Euleriens et algèbres de Hopf, Exposition. Math., Tome 12 (1994), pp. 165-178 | MR 1274784 | Zbl 0807.17003

[34] Mac Lane, S. Homology, Springer-Verlag, Grund. der Math. Wiss., Tome 114 (1963) | MR 1344215

[35] Markl, M. Distributive laws and Koszulness, Ann. Inst. Fourier, Tome 46 (1996), pp. 307-323 | Article | Numdam | MR 1393517 | Zbl 0853.18005

[36] Markl, M.; Shnider, S.; Stasheff, J. Operads in algebra, topology and physics, American Mathematical Society, Mathematical Surveys and Monographs, Tome 96 (2002) | MR 1898414 | Zbl 1017.18001

[37] Oh, S.-Q. Poisson enveloping algebras, Comm. Algebra, Tome 27 (1999), pp. 2181-2186 | Article | MR 1683858 | Zbl 0936.16020

[38] Patras, F. Construction géométrique des idempotents Euleriens. Filtration des groupes de polytopes et des groupes d’homologie de Hochschild, Bull. Soc. Math. Fr., Tome 119 (1991), pp. 173-198 | Numdam | MR 1116844 | Zbl 0752.55014

[39] Patras, F. L’algèbre des descentes d’une bigèbre graduée, J. Algebra, Tome 170 (1994), pp. 547-566 | Article | MR 1302855 | Zbl 0819.16033

[40] Pirashvili, T. Hodge decomposition for higher Hochschild homology, Ann. Sci. École Norm. Sup., Tome 33 (2000), pp. 151-179 | Numdam | MR 1755114 | Zbl 0957.18004

[41] Quillen, D. Homotopical algebra, Springer-Verlag, Lecture Notes in Math., Tome 43 (1967) | MR 223432 | Zbl 0168.20903

[42] Quillen, D. Rational homotopy theory, Ann. of Math., Tome 90 (1969), pp. 205-295 | Article | MR 258031 | Zbl 0191.53702

[43] Quillen, D. On the (co)-homology of commutative rings, Amer. Math. Soc., Proc. Symp. Pure Math., Tome 17 (1970), pp. 65-87 | MR 257068 | Zbl 0234.18010

[44] Reutenauer, C. Theorem of Poincaré-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to Stirling numbers, Combinatoire énumérative, Springer-Verlag (Lecture Notes in Math.) Tome 1234 (1986), pp. 267-284 | MR 927769 | Zbl 0621.20004

[45] Reutenauer, C. Free Lie Algebras, Clarendon Press, London Math. Soc. Mon., Tome 7 (1993) | MR 1231799 | Zbl 0798.17001

[46] Rinehart, G. Differential forms on general commutative algebras, Trans. Amer. Math. Soc., Tome 108 (1963), pp. 195-222 | Article | MR 154906 | Zbl 0113.26204

[47] Schlessinger, M.; Stasheff, J. The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra, Tome 38 (1985), pp. 313-322 | Article | MR 814187 | Zbl 0576.17008

[48] Tamarkin, D. Another proof of M. Kontsevich formality theorem (1998) (prépublication arXiv :math.QA/9803025)

[49] Vaisman, I. Lectures on the geometry of Poisson manifolds, Birkhäuser, Progress in Math., Tome 118 (1994) | MR 1269545 | Zbl 0810.53019

[50] Vigué-Poirrier, M. Cyclic homology of algebraic hypersurfaces, J. Pure Appl. Algebra, Tome 72 (1991), pp. 95-108 | Article | MR 1115570 | Zbl 0732.16008

[51] Vigué-Poirrier, M. Décompositions de l’homologie cyclique des algèbres différentielles graduées commutatives, K-theory, Tome 4 (1991), pp. 255-267 | Article | MR 1116926