AI 中文总结
研究通过定义部分上同调场论及局部多向量场的提升，扩展相关过程，系统生成非半单齐次部分上同调场论例子，证实其可积系统有第二哈密顿结构猜想，还展示了与森本理论的关系。
AI 中文摘要
我们定义了关于弗罗贝尼乌斯代数的部分上同调场论的提升以及局部多向量场的相应提升，扩展了德拉·韦多瓦、洛伦佐尼和萨沃尔迪提出的提升过程。这使我们能够系统地生成非半单齐次部分上同调场论的例子，其可积系统具有第二个哈密顿结构，从而在新的非半单情形下证实了布里亚克等人关于第二个泊松括号显式公式的猜想。此外，我们展示了这些提升构造与森本将几何结构提升到与局部代数相关的无限近点的韦伊丛理论的一些关系。
英文摘要
We define the lift of a partial cohomological field theory with respect to a Frobenius algebra and the corresponding lift of local polyvector fields, extending the lift procedure proposed by Della Vedova, Lorenzoni, and Savoldi. This allows us to systematically produce examples of non-semisimple homogeneous partial cohomological field theories whose integrable systems possess a second Hamiltonian structure, thus confirming the conjecture of Buryak et al. on an explicit formula for the second Poisson bracket in new non-semisimple cases. Moreover we present some relations of these lift constructions with the Morimoto theory of the lift of geometric structures to the Weil bundle of infinitely near points associated to a local algebra.
Comments14 pages
