  Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be
the simplicial Lie group integrating g, which is simply connected in each
simplicial level. We use the 1-jet of the classifying space of G to construct,
starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is
actually a differential graded Lie algebra. The differential and the brackets
are explicitly described in terms (of a part) of the corresponding
k-hypercrossed complex structure of Ng. The result can be seen as a geometric
interpretation of Quillen's (purely algebraic) construction of the adjunction
between simplicial Lie algebras and dg-Lie algebras.
