Pre-Calabi--Yau algebras and homotopy double Poisson gebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866917003533484032 |
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| author | Leray, Johan Vallette, Bruno |
| author_facet | Leray, Johan Vallette, Bruno |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_05062 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pre-Calabi--Yau algebras and homotopy double Poisson gebras Leray, Johan Vallette, Bruno Quantum Algebra Mathematical Physics Combinatorics Category Theory Rings and Algebras 18M85, 17B, 18M70, 14A22 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. |
| title | Pre-Calabi--Yau algebras and homotopy double Poisson gebras |
| topic | Quantum Algebra Mathematical Physics Combinatorics Category Theory Rings and Algebras 18M85, 17B, 18M70, 14A22 |
| url | https://arxiv.org/abs/2203.05062 |