Leibniz代数的无限性增强
Infinity-enhancing of Leibniz algebras
摘要：
我们建立了无限增强莱布尼茨代数之间的对应关系，最近推出，以编码张量层次，和微分分次李代数，这已经在这种情况下使用。我们解释了如何任何莱布尼兹代数产生一个微分分次李代数与相应的无限增强莱布尼兹代数。此外，通过Getzler的一个定理，该微分分次李代数在其链复形的悬挂上正则地诱导出一个$L_\infty$ -代数结构.我们明确地给出了括号的所有订单，并表明他们同意从arXiv：1904.11036中的无穷增强莱布尼茨代数得到的部分结果。
英文摘要：
We establish a correspondence between infinity-enhanced Leibniz algebras, recently introduced in order to encode tensor hierarchies, and differential graded Lie algebras, which have been already used in this context. We explain how any Leibniz algebra gives rise to a differential graded Lie algebra with a corresponding infinity-enhanced Leibniz algebra. Moreover, by a theorem of Getzler, this differential graded Lie algebra canonically induces an $L_\infty$-algebra structure on the suspension of the underlying chain complex. We explicitly give the brackets to all orders and show that they agree with the partial results obtained from the infinity-enhanced Leibniz algebras in arXiv:1904.11036.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
