BV-operators and the secondary Hochschild complex

Mamta Balodi; Abhishek Banerjee; Anita Naolekar

doi:10.5802/crmath.157

Algèbre, Géométrie et Topologie

BV-operators and the secondary Hochschild complex

Mamta Balodi ¹ ; Abhishek Banerjee ¹ ; Anita Naolekar ²

¹ Department of Mathematics, Indian Institute of Science, Bangalore
² Stat-Math Unit, Indian Statistical Institute, Bangalore

Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1239-1258.

Résumé

We introduce the notion of a BV-operator $Δ = {Δ^{n} : V^{n} ⟶ V^{n - 1}}_{n \geq 0}$ on a homotopy $G$ -algebra $V^{•}$ such that the Gerstenhaber bracket on $H (V^{•})$ is determined by $Δ$ in a manner similar to the BV-formalism. As an application, we produce a BV-operator on the cochain complex defining the secondary Hochschild cohomology of a symmetric algebra $A$ over a commutative algebra $B$ . In this case, we also show that the operator $Δ^{•}$ corresponds to Connes’ operator.

Reçu le : 2020-10-14
Révisé le : 2020-11-21
Accepté le : 2020-11-23
Publié le : 2021-01-25

DOI : 10.5802/crmath.157

Classification : 16E40

Affiliations des auteurs :

Mamta Balodi ¹ ; Abhishek Banerjee ¹ ; Anita Naolekar ²

¹ Department of Mathematics, Indian Institute of Science, Bangalore
² Stat-Math Unit, Indian Statistical Institute, Bangalore

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Mamta Balodi and Abhishek Banerjee and Anita Naolekar},
     title = {BV-operators and the secondary {Hochschild} complex},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1239--1258},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.157},
     language = {en},
}

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Mamta Balodi; Abhishek Banerjee; Anita Naolekar. BV-operators and the secondary Hochschild complex. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1239-1258. doi : 10.5802/crmath.157. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.157/

Bibliographie
Cité par

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