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

Abstract

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.

10 pages, to appear in the Proceedings of the 15-th International Workshop "Lie Theory and Its Applications in Physics" (LT-15), 19-25 June 2023, Varna, Bulgaria