• 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}
}
• Published 12 May 2021
• Mathematics
• arXiv: Mathematical Physics
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…

## References

SHOWING 1-10 OF 71 REFERENCES
EXTENDED KAC–MOODY ALGEBRAS AND APPLICATIONS
• Mathematics
• 1992
We extend the notion of a Kac–Moody algebra defined on the S1 circle to super Kac–Moody algebras defined on M × GN, M being a smooth closed compact manifold of dimension greater than one, and GN the
Extended super-Kač-Moody algebras and their super-derivation algebras
• Mathematics
• 1990
We study theN-extended super-Kač-Moody algebras, i.e. extensions of the Lie algebra of the loop group over the super-circleAN. The extensions are characterized by 2-cocycles which are computed in
Representations of Lie Algebras and Partial Differential Equations
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial
A Borcherds–Kac–Moody Superalgebra with Conway Symmetry
• Mathematics
Communications in Mathematical Physics
• 2019
We construct a Borcherds Kac-Moody (BKM) superalgebra on which the Conway group Co$_0$ acts faithfully. We show that the BKM algebra is generated by the BRST-closed states in a chiral superstring
Local Charge Algebras in Quantum Chiral Models and Gauge Theories
Affine and loop algebras are analogous to local current algebras that occur in many physical field theories. Sugawara’s formulation of the chiral model is a particularly interesting case. If this
On the Representations of the Semisimple Lie Groups. I. The Explicit Construction of Invariants for the Unimodular Unitary Group in N Dimensions
It is intended in the present series of papers to discuss explicit constructive determinations of the representations of the semisimple Lie groups SUn by an extension of the Racah‐Wigner techniques
Representations of semisimple Lie groups
• Mathematics
• 2000
We keep to the notation of the preceding note.1 Since mo is reductive, there will be no essential loss of generality from the point of view of irreducible unitary representations of Mo if we assume