On Derivation of Goldman Bracket

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 \(SO(n)\).