#
Spatial realization of a Lie algebra and the Bar construction

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Yves Félix and Daniel Tanré

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.

Published 2021-03-01.

http://www.tac.mta.ca/tac/volumes/36/7/36-07.pdf

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