In an arbitrary complete differential graded Lie algebra, we construct a group operation • on L₁ such that the differential of the product of two elements is the Baker-Campbell-Hausdorff product of their differentials, i.e., d(x• y)=dx dy. We study some properties of this new structure and some applications, especially in homotopy theory, where this operation can be used to construct a Lie model for the 4-simplex. In particular, this solves, in dimension 4, a problem proposed by Lawrence and Sullivan.
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Mario Luis Fuentes (2024) studied this question.
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