%0 Journal Article
%A Campoamor Stursberg, Otto-Rudwig
%A Montigny, Marc de
%A Traubenberg, Michel Rausch de
%T An overview of generalised Kac-Moody algebras on compact real mainfolds
%D 2022
%@ 0393-0440
%U https://hdl.handle.net/20.500.14352/72059
%X A 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.
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