We give explicit formulae for differential graded Lie algebra (DGLA) models of 3-cells. In particular, for a cube and an $n$-faceted banana-shaped 3-cell with two vertices, $n$ edges each joining those two vertices and $n$ bi-gon 2-cells, we construct a model symmetric under the geometric symmetries of the cell fixing two antipodal vertices. The cube model is to be used in forthcoming work for discrete analogues of differential geometry on cubulated manifolds.

中文翻译：

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3 细胞的显式对称 DGLA 模型

我们给出了 3 单元微分分级李代数 (DGLA) 模型的明确公式。特别地，对于一个立方体和一个具有两个顶点的 $n$-faceted 香蕉形 3-cell，每个 $n$ 边连接这两个顶点和 $n$ bi-gon 2-cells，我们在固定两个对映顶点的单元的几何对称性。立方体模型将用于在立方流形上的微分几何离散模拟的即将开展的工作。