Campoamor Stursberg, Otto-RudwigMontigny, Marc deTraubenberg, Michel Rausch de2023-06-222023-06-222022-07-160393-044010.1016/j.geomphys.2022.104624https://hdl.handle.net/20.500.14352/72059A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold to a finite-dimensional Lie group, by means of complete orthonormal bases for a Hermitian inner product on the manifold and a Fourier expansion. The Peter–Weyl theorem for the case of manifolds related to compact Lie groups and coset spaces is discussed, and appropriate Hilbert bases for the space of square-integrable functions are constructed. It is shown that such bases are characterised by the representation theory of the compact Lie group, from which a complete set of labelling operator is obtained. The existence of central extensions of generalised Kac-Moody algebras is analysed using a duality property of Hermitian operators on the manifold, and the corresponding root systems are constructed. Several applications of physically relevant compact groups and coset spaces are discussed.engjournal articlehttps://doi.org/10.1016/j.geomphys.2022.104624open access512Centrally extended infinite dimensional Lie algebrasPeter-Weyl theorem and the labelling problemFourier expansion on compact manifolds and coset spacesÁlgebra1201 Álgebra