Communications in Mathematical Physics

, Volume 193, Issue 2, pp 407–448

Framed Vertex Operator Algebras, Codes and the Moonshine Module

  • Chongying Dong
  • Robert L. Griess Jr.
  • Gerald Höhn

DOI: 10.1007/s002200050335

Cite this article as:
Dong, C., Griess Jr., R. & Höhn, G. Comm Math Phys (1998) 193: 407. doi:10.1007/s002200050335


For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge ½, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge ½ are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Chongying Dong
    • 1
  • Robert L. Griess Jr.
    • 2
  • Gerald Höhn
    • 3
  1. 1.Department of Mathematics, University of California, Santa Cruz, CA 95064, USAUS
  2. 2.Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USAUS
  3. 3.Mathematisches Institut, Universität Freiburg, Eckerstr. 1, D-79104 Freiburg, GermanyDE