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n-Extended Lorentzian Kac-Moody algebras

Fring, A. ORCID: 0000-0002-7896-7161 and Whittington, S. (2020). n-Extended Lorentzian Kac-Moody algebras. Letters in Mathematical Physics, 110, pp. 1689-1710. doi: 10.1007/s11005-020-01272-2

Abstract

We investigate a class of Kac–Moody algebras previously not considered. We refer to them as n-extended Lorentzian Kac–Moody algebras defined by their Dynkin diagrams through the connection of an An Dynkin diagram to the node corresponding to the affine root. The cases n=1 and n=2 correspond to the well-studied over- and very-extended Kac–Moody algebras, respectively, of which the particular examples of E10 and E11 play a prominent role in string and M-theory. We construct closed generic expressions for their associated roots, fundamental weights and Weyl vectors. We use these quantities to calculate specific constants from which the nodes can be determined that when deleted decompose the n-extended Lorentzian Kac–Moody algebras into simple Lie algebras and Lorentzian Kac–Moody algebra. The signature of these constants also serves to establish whether the algebras possess SO(1, 2) and/or SO(3)-principal subalgebras.

Publication Type: Article
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/
Publisher Keywords: Lorentzian Kac–Moody algebras; Infinite dimensional Lie algebras; Root and weight lattices; M-theory
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 19 May 2020 15:23
URI: https://openaccess.city.ac.uk/id/eprint/24021
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