Homological Algebra
Higher order Hochschild cohomology
Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 5-10.

Following ideas of Pirashvili, we define higher order Hochschild cohomology over spheres Sd defined for any commutative algebra A and module M. When M=A, we prove that this cohomology is equipped with graded commutative algebra and degree d Lie algebra structures as well as with Adams operations. All operations are compatible in a suitable sense. These structures are related to Brane topology.

A la manière de Pirashvili, on peut associer une cohomologie de Hochschild supérieure associée aux sphères Sd définie pour toute algèbre commutative A et module M. Lorsque M=A, cette cohomologie est munie d'un produit gradué commutatif, d'un crochet de Lie de degré d et d'opérations d'Adams. Ces structures sont compatibles entre elles et sont reliées à la topologie des Branes.

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DOI: 10.1016/j.crma.2007.11.010
Ginot, Grégory 1

1 Université Paris VI, Équipe analyse algébrique, case 82, 4, place Jussieu, 75252 Paris cedex 05, France
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Ginot, Grégory. Higher order Hochschild cohomology. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 5-10. doi : 10.1016/j.crma.2007.11.010. http://www.numdam.org/articles/10.1016/j.crma.2007.11.010/

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