Associative subalgebras of the Griess algebra and related topics

Abstract

It is shown how certain idempotents in the Griess algebra generate the discrete series representations for the Virasoro algebra inside the Frenkel-Lepowsky-Meurman's moonshine module vertex operator algebra. It is also shown that each Niemeier lattice determines (in many ways) certain maximal associative subalgebras of the Griess algebra.

tex 17 pages, to appear in : Proc. of the Conference on the Monster and Lie algebras at The Ohio State University, May 1996