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
Last updated April 15th, 2018.