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

TL;DR

This paper explores the construction of generalized Kac-Moody and Virasoro algebras on the two-sphere and two-torus, showing they can be derived from standard algebras on these manifolds.

Contribution

It extends the framework of Kac-Moody and Virasoro algebras to compact manifolds like the two-sphere and two-torus, providing new geometric insights.

Findings

Algebras can be constructed on the two-sphere and two-torus.

Standard Kac-Moody and Virasoro algebras can generate these generalized algebras.

The approach links algebraic structures to geometric properties of manifolds.

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.