Comptes Rendus
no. 11-12
Algèbre, Géométrie et Topologie
BV-operators and the secondary Hochschild complex
Mamta Balodi1 ; Abhishek Banerjee1  ; Anita Naolekar2
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.

We introduce the notion of a BV-operator Δ={Δ n :V n ⟶V n-1 } n≥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.

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DOI : 10.5802/crmath.157
Classification : 16E40
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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     title = {BV-operators and the secondary {Hochschild} complex},
     journal = {Comptes Rendus. Math\'ematique},
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     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
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     year = {2020},
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     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/

[1] Mamta Balodi; Abhishek Banerjee; Anita Naolekar Weak comp algebras and cup products in secondary Hochschild cohomology of entwining structures (2020) (https://arxiv.org/abs/1909.05476v3)

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[5] Murray Gerstenhaber; Alexander A. Voronov Homotopy G-algebras and moduli space operad, Int. Math. Res. Not., Volume 1995 (1995) no. 3, pp. 141-153 | DOI | MR | Zbl

[6] Yvette Kosmann-Schwarzbach Quasi, twisted, and all that...in Poisson geometry and Lie algebroid theory, The breadth of symplectic and Poisson geometry (Progress in Mathematics), Volume 232, Birkhäuser, 2005, pp. 363-389 | DOI | MR | Zbl

[7] Jean-Louis Koszul Crochet de Schouten–Nijenhuis et cohomologie, The mathematical heritage of Élie Cartan (Lyon, 1984) (Astérisque), Société Mathématique de France, 1985, pp. 257-271 | Numdam | Zbl

[8] Jacob Laubacher; Mihai D. Staic; Alin Stancu Bar simplicial modules and secondary cyclic (co)homology, J. Noncommut. Geom., Volume 12 (2018) no. 3, pp. 865-887 | DOI | MR | Zbl

[9] Mihai D. Staic Secondary Hochschild cohomology, Algebr. Represent. Theory, Volume 19 (2016) no. 1, pp. 47-56 | DOI | MR | Zbl

[10] Mihai D. Staic; Alin Stancu Operations on the secondary Hochschild cohomology, Homology Homotopy Appl., Volume 17 (2015) no. 1, pp. 129-146 | DOI | MR | Zbl

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