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PRE-CALABI-YAU ALGEBRAS AND HOMOTOPY DOUBLE POISSON GEBRAS

Abstract : We prove that the notion of a curved pre-Calabi-Yau algebra is equivalent to the notion of a curved homotopy double Poisson gebra, thereby settling the equivalence between the two ways to define derived noncommutative Poisson structures. We actually prove that the respective differential graded Lie algebras controlling both deformation theories are isomorphic.This allows us to apply the recent developments of the properadic calculus in order to establish the homotopical properties of curved pre-Calabi-Yau algebras: infinity-morphisms, homotopy transfer theorem, formality, Koszul hierarchy, and twisting procedure.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03605677
Contributor : Bruno Vallette Connect in order to contact the contributor
Submitted on : Friday, March 11, 2022 - 11:31:10 AM
Last modification on : Wednesday, April 27, 2022 - 4:59:10 AM

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  • HAL Id : hal-03605677, version 1

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Johan Leray, Bruno Vallette. PRE-CALABI-YAU ALGEBRAS AND HOMOTOPY DOUBLE POISSON GEBRAS. 2022. ⟨hal-03605677⟩

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