• Corpus ID: 234469878

An overview of generalised Kac-Moody algebras on compact real manifolds

@article{CampoamorStursberg2021AnOO,
  title={An overview of generalised Kac-Moody algebras on compact real manifolds},
  author={Rutwig Campoamor-Stursberg and Marc de Montigny and Michel Rausch de Traubenberg},
  journal={arXiv: Mathematical Physics},
  year={2021}
}
A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold $\mathcal{M}$ 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 $L^{2}(\mathcal{M})$ of square-integrable functions are constructed. It is shown that… 
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