2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224757We give a summary of R. Borcherds' solution (with some modifications) to the following part of the Conway-Norton conjectures: Given the Monster simple group and Frenkel-Lepowsky-Meurman's moonshine module for the group, prove the equality between the graded characters of the elements of the Monster group acting on the module (i.e., the McKay-Thompson series) and the modular functions provided by Conway and Norton. The equality is established using the homology of a certain subalgebra of the monster Lie algebra, and the Euler-Poincare identity.First presented at Moonshine - the first quarter century and beyond.A Workshop on the Moonshine Conjectures and Vertex Algebras ICMS, 5 - 13 July 2004Representation TheoryGroup Theory1706text