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Symmetric Lie models of a triangle

Volume 246 / 2019

Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré Fundamenta Mathematicae 246 (2019), 289-300 MSC: Primary 55P62; Secondary 17B01, 55U10. DOI: 10.4064/fm518-7-2018 Published online: 15 February 2019


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 $\varSigma _2$ 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.


  • Urtzi BuijsDepartamento de Álgebra, Geometría y Topología
    Universidad de Málaga
    Ap. 59
    29080 Málaga, Spain
  • Yves FélixInstitut de Mathématiques et Physique
    Université Catholique de Louvain-la-Neuve
    Louvain-la-Neuve, Belgium
  • Aniceto MurilloDepartamento de Álgebra, Geometría y Topología
    Universidad de Málaga
    Ap. 59, 29080-Málaga, Spain
  • Daniel TanréDépartement de Mathématiques, UMR 8524
    Université de Lille 1
    59655 Villeneuve d’Ascq Cedex, France

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