Kac-Moody and Virasoro algebras on the two-sphere and the two-torus

We particularise the construction of generalised Kac-Moody algebras associated to compact real manifolds to the case of the two-torus ${\mathbb{T}}_2$ and the two-sphere ${\mathbb{S}}^2$. It is shown that these algebras, as well as a Virasoro algebra associated to the two-torus and the two-sphere, can also be derived considering the usual Kac-Moody and Virasoro algebras.