  Let $G \to P \to M$ be a flat principal bundle over a closed and oriented
manifold $M$ of dimension $m=2d$. We construct a map of Lie algebras $\Psi:
\H_{2\ast} (L M) \to {\o}(\Mc)$, where $\H_{2\ast} (LM)$ is the even
dimensional part of the equivariant homology of $LM$, the free loop space of
$M$, and $\Mc$ is the Maurer-Cartan moduli space of the graded differential Lie
algebra $\Omega^\ast (M, \adp)$, the differential forms with values in the
associated adjoint bundle of $P$. For a 2-dimensional manifold $M$, our Lie
algebra map reduces to that constructed by Goldman in \cite{G2}. We treat
different Lie algebra structures on $\H_{2\ast}(LM)$ depending on the choice of
the linear reductive Lie group $G$ in our discussion.
