Generalisation of affine Lie algebras on compact real manifolds

TL;DR

This paper explores a new class of generalized Kac-Moody algebras constructed from differentiable maps on compact manifolds, extending the algebraic framework to more complex geometric settings.

Contribution

It introduces a novel generalization of affine Lie algebras using differentiable mappings on compact manifolds, broadening the scope of algebraic structures in geometry.

Findings

Defined new algebraic structures based on differentiable mappings

Extended the theory of affine Lie algebras to compact manifolds

Potential applications in mathematical physics and geometry

Abstract

We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.