论文标题
双准波森代数是前卡拉比YAU
Double quasi-Poisson algebras are pre-Calabi-Yau
论文作者
论文摘要
在本文中，我们证明了两次准脉代代数，这些代数是准 - 波森歧管的非共同类似物，自然会引起喀拉比前的代数。这扩展了[11]中的主要结果之一（另请参见[10]），其中发现了卡拉比YAU代数与双泊松代数之间的关系。但是，在上述文章中构建的卡拉比前代数与这项工作中构建的代数之间的主要区别在于，较高的乘法是由较高的乘法由$ a _ {\ infty} $的整数所索引的较高的乘法，这是由友好的algebra与友好的algebra相关的代数结构。乘以涉及Bernoulli数字的明确确定的系数。
In this article we prove that double quasi-Poisson algebras, which are non-commutative analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one of the main results in [11] (see also [10]), where a relationship between pre-Calabi-Yau algebras and double Poisson algebras was found. However, a major difference between the pre-Calabi-Yau algebra constructed in the mentioned articles and the one constructed in this work is that the higher multiplications indexed by even integers of the underlying $A_{\infty}$-algebra structure of the pre-Calabi-Yau algebra associated to a double quasi-Poisson algebra do not vanish, but are given by nice cyclic expressions multiplied by explicitly determined coefficients involving the Bernoulli numbers.
