Let $\Sigma_{g}$ be a closed oriented surface of genus $g$, Goldman defined a Lie algebra structure on the free module generated by the free homotopy
classes of loops on $\Sigma_{g}$. Roughly speaking, the Lie bracket is defined via intersection and concatenation of loops. In detail, see his paper *Invariant functions on Lie groups and Hamiltonian flows of surface group representations* .

I want to know that are there any formulas to compute this Lie bracket for small nonzero $g$? For example, what is the Goldman Lie algebra of torus? Any help or any references would be very appreciated.