论文标题
累积物，Koszul支架和同源扰动理论，用于交换$ bv_ \ infty $和$ ibl_ \ infty $代数
Cumulants, Koszul brackets and homological perturbation theory for commutative $BV_\infty$ and $IBL_\infty$ algebras
论文作者
论文摘要
我们探讨了累积剂和Koszul支架的经典结构之间的关系，这表明前者是后者的外科版本。此外，在一些其他技术假设下，我们证明这两种结构都与标准同源扰动理论兼容。作为这些结果的应用，我们为$ l_ \ infty $和$ ibl_ \ inby $ ngebras的同拷贝传输定理提供了新的证明，基于对称张量的技巧和标准扰动lemma，就像$ a_ \ infty $ elgebras的常用方法一样。此外，从Kravchenko的意义上讲，我们证明了合格的$ bv_ \ infty $代数转移定理，这似乎是新的。在此过程中，我们介绍了通勤$ bv_ \ infty $代数之间的新定义。
We explore the relationship between the classical constructions of cumulants and Koszul brackets, showing that the former are an expontial version of the latter. Moreover, under some additional technical assumptions, we prove that both constructions are compatible with standard homological perturbation theory in an appropriate sense. As an application of these results, we provide new proofs for the homotopy transfer Theorem for $L_\infty$ and $IBL_\infty$ algebras based on the symmetrized tensor trick and the standard perturbation Lemma, as in the usual approach for $A_\infty$ algebras. Moreover, we prove a homotopy transfer Theorem for commutative $BV_\infty$ algebras in the sense of Kravchenko which appears to be new. Along the way, we introduce a new definition of morphism between commutative $BV_\infty$ algebras.
