论文标题
F-manifold代数和通过前代数的变形量化
F-manifold algebras and deformation quantization via pre-Lie algebras
论文作者
论文摘要
F-manifold代数的概念是$ f $ - manifold的基础代数结构。我们介绍了交换性代数的前LIE形式变形的概念，并表明F-Manifold代数是相应的半古典限制。我们研究了前lie n构想的前lie无限变形，并扩展到前lie（n+1） - 通过lie代数的共同体学组对换向性缔合代数的形成。我们介绍了f前曼膜前代数和双F-f-manifold代数的概念，并表明F-F-manifold代数会引起F-Manifold代数通过次级附属的关联代数和亚副标。我们使用Rota-baxter操作员，更普遍的O-操作器和F-Manifold代数上的平均操作员来构建F-F-Manifold代数和双F-F前f-manifold代数。
The notion of an F-manifold algebra is the underlying algebraic structure of an $F$-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding semi-classical limits. We study pre-Lie infinitesimal deformations and extension of pre-Lie n-deformation to pre-Lie (n+1)-deformation of a commutative associative algebra through the cohomology groups of pre-Lie algebras. We introduce the notions of pre-F-manifold algebras and dual pre-F-manifold algebras, and show that a pre-F-manifold algebra gives rise to an F-manifold algebra through the sub-adjacent associative algebra and the sub-adjacent Lie algebra. We use Rota-Baxter operators, more generally O-operators and average operators on F-manifold algebras to construct pre-F-manifold algebras and dual pre-F-manifold algebras.
