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.

中文翻译：

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莱布尼茨代数的无穷增强

我们建立了无穷增强的莱布尼茨代数（最近引入以对张量层次结构进行编码）和微分分级李代数之间的对应关系，后者已在此上下文中使用。我们解释了任何莱布尼茨代数如何产生具有相应无穷大增强的莱布尼茨代数的微分分级李代数。此外，根据 Getzler 定理，这个微分分级李代数在底层链复合体的悬浮上规范地归纳出 $L_\infty$-代数结构。我们明确地为所有阶加上括号，并表明它们与 arXiv:1904.11036 中从无穷大增强的莱布尼茨代数中获得的部分结果一致。