Symmetric Lie models of a triangle
Tom 246 / 2019
Fundamenta Mathematicae 246 (2019), 289-300
MSC: Primary 55P62; Secondary 17B01, 55U10.
DOI: 10.4064/fm518-7-2018
Opublikowany online: 15 February 2019
Streszczenie
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 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 \varSigma _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.
