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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 $$SO(n)$$.

### Most cited references13

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### Quantum field theory and the Jones polynomial

(1989)
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### Topological sigma models

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

(1986)
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### Author and article information

###### Journal
2013-10-16
2016-01-14
###### Article
1310.4519