三角形的显式对称DGLA模型
An explicit symmetric DGLA model of a triangle
摘要：
本文给出了三角形的微分分次李代数（DGLA）模型的显式公式，该模型在胞腔的几何对称性下是对称的。这是继劳伦斯-沙利文的工作（唯一）DGLA模型的间隔和加迪什-格里尼亚斯蒂-劳伦斯的一个明确的对称模型的双边形。与双边形的情况一样，基本的中间步骤是构造对称点。虽然在这种由莫雷-嘉当方程的解给出的点和由零阶李代数元素的规范变换给出的线的扭曲几何中，三角形的中线是不重合的，但可以进行各种其他尺规作图法。该构造同样可用于给出任意$k$ -矩阵的对称模型。
英文摘要：
We give explicit formulae for a differential graded Lie algebra (DGLA) model of the triangle which is symmetric under the geometric symmetries of the cell. This follows the work of Lawrence-Sullivan on the (unique) DGLA model of the interval and of Gadish-Griniasty-Lawrence on an explicit symmetric model of the bi-gon. As in the case of the bi-gon, the essential intermediate step is the construction of a symmetric point. Although in this warped geometry of points given by solutions of the Maurer-Cartan equation and lines given by a gauge transformation by Lie algebra elements of grading zero, the medians of a triangle are not concurrent, various other geometric constructions can be carried out. The construction can similarly be applied to give symmetric model of arbitrary $k$-gons.
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。
