论文标题
前卡拉比 - YAU代数和同型双泊松Gebras
Pre-Calabi--Yau algebras and homotopy double Poisson gebras
论文作者
论文摘要
我们证明，弯曲的前calabi-YAU代数的概念等于弯曲的同型双泊松Gebra的概念，从而解决了定义派生的非交互性泊松结构的两种方法之间的等价。 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.
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.
