Homological algebra/Mathematical physics
The obstruction to the existence of a loopless star product
Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 881-883.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.018
Willwacher, Thomas 1

1 Department of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
@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] Bayen, F.; Flato, M.; Fronsdal, C.; Lichnerowicz, A.; Sternheimer, D. Deformation theory and quantization. I. Deformations of symplectic structures, Ann. Phys., Volume 111 (1978) no. 1, pp. 61-110

[2] Dito, G. The necessity of wheels in universal quantization formulas, 2013 | arXiv

[3] Kontsevich, M. Deformation quantization of Poisson manifolds, Lett. Math. Phys., Volume 66 (2003) no. 3, pp. 157-216

[4] S. Merkulov, Personal communication.

[5] Penkava, M.; Vanhaecke, P. Deformation quantization of polynomial Poisson algebras, J. Algebra, Volume 227 (2000) no. 1, pp. 365-393

[6] Shoikhet, B. An L algebra structure on polyvector fields, 2008 | arXiv

[7] Van den Bergh, M. The Kontsevich weight of a wheel with spokes pointing outward, Algebr. Represent. Theory, Volume 12 (2009), pp. 443-479 | DOI

[8] Willwacher, Thomas A counterexample to the quantizability of modules, Lett. Math. Phys., Volume 81 (2007) no. 3, pp. 265-280

Cité par Sources :