**An explicit symmetric DGLA model of a triangle**

**Itay Griniasty and Ruth Lawrence**

**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 (unique0 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 constructuion can similarly be applied to give symmetric models of arbitrary k-gons.

**Keywords: **DGLA, infinity structure, Maurer-Cartan, Baker-Campbell-Hausdorff formula

**AMS subject classification: **17B55 17B01 55U15

**Length: **17 pages

**Reference: ** Submitted

You can download this paper from arXiv:math1802.02795 or from here.

*Last updated April 15th, 2018.*

ruthel@math.huji.ac.il