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Borcherds and Kac-Moody extensions of simple finite-dimensional Lie algebras
Physique Théorique et Mathématique, Université Libre de Bruxelles & International Solvay Institutes, Bruxelles, Belgium.
2012 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 6, article id 003Article in journal (Refereed) Published
Abstract [en]

We study the Borcherds superalgebra obtained by adding an odd (fermionic) null root to the set of simple roots of a simple finite-dimensional Lie algebra. We compare it to the Kac-Moody algebra obtained by replacing the odd null root by an ordinary simple root, and then adding more simple roots, such that each node that we add to the Dynkin diagram is connected to the previous one with a single line. This generalizes the situation in maximal supergravity, where the E-n symmetry algebra can be extended either to a Borcherds superalgebra or to the kac-Moody algebra E-11, and both extensions can be used to derive the spectrum of p-form potentials in the theory. We show that also in the general case, the Borcherds and Kac-Moody extensions lead to the same 'p-form spectrum' of representations of the simple finite-dimensional Lie algebra.

Place, publisher, year, edition, pages
Springer, 2012. no 6, article id 003
Keywords [en]
Supergravity Models, M-Theory
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:oru:diva-111167DOI: 10.1007/JHEP06(2012)003ISI: 000306416500008Scopus ID: 2-s2.0-84864373816OAI: oai:DiVA.org:oru-111167DiVA, id: diva2:1832111
Note

The work is supported by IISN - Belgium (conventions 4.4511.06 and 4.4514.08), by the Belgian Federal Science Policy Office through the Interuniversity Attraction Pole P6/11.

Available from: 2024-01-28 Created: 2024-01-28 Last updated: 2024-02-12Bibliographically approved

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Palmkvist, Jakob

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