We prove that the spatial realization of a rational complete Lie algebra L, concentrated in degree 0, is isomorphic to the simplicial bar construction on the group, obtained from the Baker-Campbell-Hausdorff product on L.
Keywords: rational homotopy theory, realization of Lie algebras, Lie models of simplicial sets, simplicial bar construction
2020 MSC: 55P62, 17B55, 55U10
Theory and Applications of Categories, Vol. 36, 2021, No. 7, pp 201-205.