三角形的对称Lie模型
Symmetric Lie models of a triangle
摘要：
R. Lawrence和D. Sullivan从平坦连接和规范变换流的几何思想出发，构造了一个区间的Lie模型。他们的模型支持对称群$Σ_2$的作用，反映了区间的几何对称性。本文提出了一个三角形的Lie模型，它的对称群$Σ_3$的作用与三角形的几何对称性相容.我们还证明了由具有$k$顶点的电路组成的图的模型通过图的自同构允许Maurer-Cartan元稳定。
英文摘要：
R. Lawrence and D. Sullivan have constructed a Lie model for an interval from the geometrical idea of flat connections and flows of gauge transformations. Their model supports an action of the symmetric group $Σ_2$ reflecting the geometrical symmetry of the interval. In this work, we present a Lie model of the triangle with an action of the symmetric group $Σ_3$ compatible with the geometrical symmetries of the triangle. We also prove that the model of a graph consisting of a circuit with $k$ vertices admits a Maurer-Cartan element stable by the automorphisms of the graph.
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