  In this paper, we obtain an infinite dimensional Lie algebra of exotic gauge
invariant observables that is closed under Goldman-type bracket associated with
monodromy matrices of flat connections on a compact Riemann surface for $G_{2}$
gauge group. As a by-product, we give an alternative derivation of known
Goldman bracket for classical gauge groups $GL(n,\mathbb{R})$,
$SL(n,\mathbb{R})$, $U(n)$, $SU(n)$, $Sp(2n,\mathbb{R})$ and $SO(n)$.
