论文标题
$ f $ - 代理和通过前代代数量化的变形量化
$F$-algebroids and deformation quantization via pre-Lie algebroids
论文作者
论文摘要
在本文中，首先，我们引入了$ f $ -Algebroids的概念的新方法，这是$ f $ -Manifold代数和$ f $ -Manifolds的概括，并表明$ f $ -Algebroids是相应的半古典限制，对通勤交流的预先形式上的AlgeBroids的预先形式化。然后，我们使用前代代数的变形共同体来研究前lie无限变形，并扩展前$ n $ n $ deformation to pree $（n+1）$ - 交换式代数的变形。接下来，我们发展了杜布罗文（Dubrovin）的二元性二元性二元性二元性二元性，并最终具有身份，并在$ f $ -Algebroids上使用nijenhuis运营商来构建新的$ f $ algebroids。最后，我们介绍了前$ f $ -Algebroids的概念，这是具有兼容平坦连接的$ f $ - manifolds的概括。讨论了Dubrovin的二$ F $ -F $ - 代数，最终具有身份，Nijenhuis运营商对Pre-F $ -F $ -Algebroids及其在整体系统中的应用。
In this paper, first we introduce a new approach to the notion of $F$-algebroids, which is a generalization of $F$-manifold algebras and $F$-manifolds, and show that $F$-algebroids are the corresponding semi-classical limits of pre-Lie formal deformations of commutative associative algebroids. Then we use the deformation cohomology of pre-Lie algebroids to study pre-Lie infinitesimal deformations and extension of pre-Lie $n$-deformations to pre-Lie $(n+1)$-deformations of a commutative associative algebroid. Next we develop the theory of Dubrovin's dualities of $F$-algebroids with eventual identities and use Nijenhuis operators on $F$-algebroids to construct new $F$-algebroids. Finally we introduce the notion of pre-$F$-algebroids, which is a generalization of $F$-manifolds with compatible flat connections. Dubrovin's dualities of pre-$F$-algebroids with eventual identities, Nijenhuis operators on pre-$F$-algebroids and their applications to integral systems are discussed.
