An explicit symmetric DGLA model of a triangle

Itay Griniasty; Ruth Lawrence

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arXiv · 1802.02795

An explicit symmetric DGLA model of a triangle

Itay Griniasty·Ruth Lawrence

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Abstract

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.

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Itay Griniasty, Ruth Lawrence. 2018-02-08. An explicit symmetric DGLA model of a triangle. https://arxiv.org/abs/1802.02795

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