THE MONSTER LIE-ALGEBRA

We calculate the multiplicities of all the roots of the "monster Lie algebra." This gives an example of a Lie algebra all of whose simple roots and root multiplicities are known and which is not finite dimensional or an affine Kac-Moody algebra. There seem to be several similar infinite dimensional Lie algebras, which to a sympathetic eye appear to correspond to some of the sporadic simple groups. © 1990.