On définit une structure de BV sur la cohomologie de Hochschild d’une algèbre associative unitaire munie d’une forme bilinéaire symétrique non dégénérée. La structure d’algèbre de Gerstenhaber induite est celle introduite dans l’article originel de Gerstenhaber sur la cohomologie de Hochschild. On étend ce résultat au cas d’une algèbre -infinie unitaire munie d’une forme bilinéaire symétrique -infinie non dégénérée.
We define a BV-structure on the Hochschild cohomology of a unital, associative algebra with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital -algebra with a symmetric and non-degenerate -inner product.
Keywords: Hochschild cohomology, Batalin Vilkovisky algebra
Mot clés : cohomologie de Hochschild, algèbre de Batalin Vilkovisky
@article{AIF_2008__58_7_2351_0, author = {Tradler, Thomas}, title = {The {Batalin-Vilkovisky} {Algebra} on {Hochschild} {Cohomology} {Induced} by {Infinity} {Inner} {Products}}, journal = {Annales de l'Institut Fourier}, pages = {2351--2379}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {7}, year = {2008}, doi = {10.5802/aif.2417}, mrnumber = {2498354}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2417/} }
TY - JOUR AU - Tradler, Thomas TI - The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products JO - Annales de l'Institut Fourier PY - 2008 SP - 2351 EP - 2379 VL - 58 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2417/ DO - 10.5802/aif.2417 LA - en ID - AIF_2008__58_7_2351_0 ER -
%0 Journal Article %A Tradler, Thomas %T The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products %J Annales de l'Institut Fourier %D 2008 %P 2351-2379 %V 58 %N 7 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2417/ %R 10.5802/aif.2417 %G en %F AIF_2008__58_7_2351_0
Tradler, Thomas. The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products. Annales de l'Institut Fourier, Tome 58 (2008) no. 7, pp. 2351-2379. doi : 10.5802/aif.2417. http://archive.numdam.org/articles/10.5802/aif.2417/
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