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Pré-Publication, Document De Travail Année : 2023

Homotopy Transfer Theorem and minimal models for pre-Calabi-Yau algebras

Marion Boucrot
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Résumé

In this article we prove that given quasi-isomorphic dg vector spaces and a pre-Calabi-Yau structure on one of them there exists a pre-Calabi-Yau structure on the other as well as a pre-Calabi-Yau morphism between the two. This extends the Homotopy Transfer Theorem proved by T. Kadeishvili and a similar result of D. Petersen. Moreover, we show that a pre-Calabi-Yau morphism whose first component is an isomorphism of dg vector spaces is a pre-Calabi-Yau isomorphism, i.e. the inverse of the isomorphism of dg vector spaces extends to an inverse of the pre-Calabi-Yau morphism. We incidentally show that any pre-Calabi-Yau algebra has a minimal model. Finally, we prove that any quasi-isomorphism of pre-Calabi-Yau algebras admits a quasi-inverse.
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Dates et versions

hal-04135543 , version 1 (21-06-2023)
hal-04135543 , version 2 (05-07-2023)

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  • HAL Id : hal-04135543 , version 2

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Marion Boucrot. Homotopy Transfer Theorem and minimal models for pre-Calabi-Yau algebras. 2023. ⟨hal-04135543v2⟩
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