We show that the center of the Goldman Lie algebra associated to a closed orientable surface is generated by the class of the trivial loop. For an orientable nonclosed surface of finite type, the center is generated by closed curves which are either homotopically trivial or homotopic to boundary components or punctures.
"Center of the Goldman Lie algebra." Algebr. Geom. Topol. 16 (5) 2839 - 2849, 2016. https://doi.org/10.2140/agt.2016.16.2839