Consider a closed non-degenerate 3-form ω with an infinitesimal action of a Lie algebra $\mathfrak{g}$. Motivated by the fact that the observables associated to ω form a Lie 2-algebra, we introduce homotopy moment maps defined on a Lie 2-algebra rather than just on the Lie algebra $\mathfrak{g}$.

We formulate existence criteria and provide a construction for such homotopy moment maps, by characterizing them in terms of cohomology.

中文翻译：

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多辛几何中的李2代数矩图

考虑具有李代数的极小作用的闭合非简并3形式ω$\mathfrak{G}$。受与ω相关的可观观测物形成李2代数的事实的启发，我们引入了在李2代数而不是仅在李2代数上定义的同伦矩图$\mathfrak{G}$。

我们制定了存在标准，并通过用同调性对其进行表征，为此类同伦矩图提供了一种构造。