RT Journal Article
T1 An overview of generalised Kac-Moody algebras on compact real mainfolds
A1 Campoamor Stursberg, Otto-Rudwig
A1 Montigny, Marc de
A1 Traubenberg, Michel Rausch de
AB 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.
PB Elsevier
SN 0393-0440
YR 2022
FD 2022-07-16
LK https://hdl.handle.net/20.500.14352/72059
UL https://hdl.handle.net/20.500.14352/72059
LA eng
NO Ministerio de Ciencia, Innovación y Universidades (España)/Fondo Europeo de Desarrollo Regional
NO Natural Sciences and Engineering Research Council
DS Docta Complutense
RD 3 jul 2025