Realizations of the Monster Lie algebra
| dc.creator | Jurisich, Elizabeth | |
| dc.creator | Lepowsky, James | |
| dc.creator | Wilson, R. L. | |
| dc.date | 1994-08-05 | |
| dc.date.accessioned | 2026-07-07T09:14:22Z | |
| dc.date.available | 2026-07-07T09:14:22Z | |
| dc.description | We study aspects of the theory of generalized Kac-Moody Lie algebras (or Borcherds algebras) and their standard modules. It is shown how such an algebra with no mutually orthogonal imaginary simple roots, including Borcherds' Monster Lie algebra $\frak m$, can be naturally constructed from a certain Kac-Moody subalgebra and a module for it. We observe that certain generalized Verma (induced) modules for generalized Kac-Moody algebras are standard modules and hence irreducible. In particular, starting from the moonshine module for the Monster group $M$, we construct a certain $\{frak gl}_2$- and $M$-module, the tensor algebra over which carries a natural structure of irreducible module for $\frak m$, which is realized as an explicitly prescribed $M$-covariant Lie algebra of operators on this tensor algebra. The existence of large free subalgebras of $\frak m$ is further exploited to provide a simplification of Borcherds' proof of the Conway-Norton conjectures for the McKay-Thompson series of the moonshine module. The coefficients of these series are shown to satisfy natural recursion relations (replication formulas) equivalent to, but different from, those obtained by Borcherds. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/9408037 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9408037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152646 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Realizations of the Monster Lie algebra | |
| dc.type | text |