Spatial realization of a Lie algebra and Bar construction of a group

Abstract

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 $L$.

References in corpus (3)

• Representing the deformation $\infty$-groupoid
• Homotopy theory of complete Lie algebras and Lie models of simplicial sets
• The infinity Quillen functor, Maurer-Cartan elements and DGL realizations