Framed Vertex Operator Algebras, Codes and the Moonshine Module |
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Authors: | Chongying Dong Robert L Griess Jr Gerald Höhn |
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Institution: | Department of Mathematics, University of California, Santa Cruz, CA 95064, USA, US Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA, US Mathematisches Institut, Universit?t Freiburg, Eckerstr. 1, D-79104 Freiburg, Germany, DE
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Abstract: | For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge ?,
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 ? are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra
is obtained for a distinguished system of 48 Virasoro algebras.
Received: 14 July 1997 / Accepted: 8 September 1997 |
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