Resumen de Realizations of the Monster Lie algebra
Elizabeth Jurisich, James Lepowsky, Robert L. Wilson
In this paper we reinterpret the theory of generalized Kac-Moody Lie algebras in terms of local Lie algebras formed from reductive or Kac-Moody algebras and certain modules (possibly infinite-dimensional) for these algebras. We exploit the fact, established in [19], that certain generalized Kae-Moody algebras contain specific large free subalgebras, in order to exhibit these generalizedKac-Moody algebras as explicitly prescribed Lie algebras of operators acting on tensor algebras. In the most important special case, that of R. Borcherds' Monster Lie algebra m, introduced in [4] (see a~so [5]), we apply the free subalgebra result [19] to simplify Boreherds' work [4] on the Conway-Norton conjectures (see [8]) for the "moonshine module" V~ ([11], [12]) for the Fiseher-Griess Monster group M. In particular, we realize m as an explicitly prescribed M-covariant Lie algebra of operators acting on the tensor algebra over a certain g[2- and M-module built in a simple way from the M-module V ~ .
