Framed vertex operator algebras, codes and the moonshine module

Details Framed vertex operator algebras, codes and the moonshine module Framed vertex operator algebras, codes and the moonshine module

1997-07-07

arxiv.org/abs/q-alg/9707008v1

Comm. Math. Phys. 193 (1998), 407-448

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 54 pages

Scientific paper

10.1007/s002200050335

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, 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 1/2 are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras.

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