Subalgebras of Hyperbolic Kac-Moody Algebras
| dc.creator | Feingold, Alex J. | |
| dc.creator | Nicolai, Hermann | |
| dc.date | 2003-03-14 | |
| dc.date.accessioned | 2026-07-07T04:56:04Z | |
| dc.date.available | 2026-07-07T04:56:04Z | |
| dc.description | The hyperbolic (and more generally, Lorentzian) Kac-Moody (KM) Lie algebras $\cA$ of rank $r+2 > 2$ are shown to have a rich structure of indefinite KM subalgebras which can be described by specifying a subset of positive real roots of $\cA$ such that the difference of any two is not a root of $\cA$. Taking these as the simple roots of the subalgebra gives a Cartan matrix, generators and relations for the subalgebra. Applying this to the canonical example of a rank 3 hyperbolic KM algebra, $\cF$, we find that $\cF$ contains all of the simply laced rank 2 hyperbolics, as well as an infinite series of indefinite KM subalgebras of rank 3. It is shown that $\cA$ also contains Borcherds algebras, obtained by taking all of the root spaces of $\cA$ whose roots are in a hyperplane (or any proper subspace). This applies as well to the case of rank 2 hyperbolics, where the Borcherds algebras have all their roots on a line, giving the simplest possible examples. | |
| dc.description | 18 pages, 2 figures, LaTeX using Contemporary Math proceedings style file | |
| dc.identifier | https://arxiv.org/abs/math/0303179 | |
| dc.identifier | http://arxiv.org/abs/math/0303179 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66792 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | 17B67;81R10 | |
| dc.title | Subalgebras of Hyperbolic Kac-Moody Algebras | |
| dc.type | text |