Nous montrons qu'il y a une obstruction à l'éxistence d'une produit étoile défini par les graphes de Kontsevich sans cycle orienté.
We show that there is an obstruction to the existence of a star product defined by Kontsevich graphs without directed cycles.
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@article{CRMATH_2014__352_11_881_0, author = {Willwacher, Thomas}, title = {The obstruction to the existence of a loopless star product}, journal = {Comptes Rendus. Math\'ematique}, pages = {881--883}, publisher = {Elsevier}, volume = {352}, number = {11}, year = {2014}, doi = {10.1016/j.crma.2014.09.018}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2014.09.018/} }
TY - JOUR AU - Willwacher, Thomas TI - The obstruction to the existence of a loopless star product JO - Comptes Rendus. Mathématique PY - 2014 SP - 881 EP - 883 VL - 352 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.09.018/ DO - 10.1016/j.crma.2014.09.018 LA - en ID - CRMATH_2014__352_11_881_0 ER -
%0 Journal Article %A Willwacher, Thomas %T The obstruction to the existence of a loopless star product %J Comptes Rendus. Mathématique %D 2014 %P 881-883 %V 352 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.09.018/ %R 10.1016/j.crma.2014.09.018 %G en %F CRMATH_2014__352_11_881_0
Willwacher, Thomas. The obstruction to the existence of a loopless star product. Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 881-883. doi : 10.1016/j.crma.2014.09.018. http://www.numdam.org/articles/10.1016/j.crma.2014.09.018/
[1] Deformation theory and quantization. I. Deformations of symplectic structures, Ann. Phys., Volume 111 (1978) no. 1, pp. 61-110
[2] The necessity of wheels in universal quantization formulas, 2013 | arXiv
[3] Deformation quantization of Poisson manifolds, Lett. Math. Phys., Volume 66 (2003) no. 3, pp. 157-216
[4] S. Merkulov, Personal communication.
[5] Deformation quantization of polynomial Poisson algebras, J. Algebra, Volume 227 (2000) no. 1, pp. 365-393
[6] An algebra structure on polyvector fields, 2008 | arXiv
[7] The Kontsevich weight of a wheel with spokes pointing outward, Algebr. Represent. Theory, Volume 12 (2009), pp. 443-479 | DOI
[8] A counterexample to the quantizability of modules, Lett. Math. Phys., Volume 81 (2007) no. 3, pp. 265-280
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