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      On Derivation of Goldman Bracket

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          Abstract

          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 \(SO(n)\).

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          Most cited references 13

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          Quantum field theory and the Jones polynomial

           Edward Witten (1989)
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            Topological sigma models

             Edward Witten (1988)
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              Invariant functions on Lie groups and Hamiltonian flows of surface group representations

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                Author and article information

                Journal
                2013-10-16
                2016-01-14
                Article
                1310.4519
                5bdcaa5a-ef4e-408c-b6ad-8db5a9d28157

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                JHEP02 (2016) 001
                35 pages, possible applications added to the introduction, references added ,accepted version to appear in JHEP
                math-ph hep-th math.MP

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