A nonmeromorphic extension of the moonshine module vertex operator algebra
Abstract
Description
We describe a natural structure of an abelian intertwining algebra (in the sense of Dong and Lepowsky) on the direct sum of the untwisted vertex operator algebra constructed {}from the Leech lattice and its (unique) irreducible twisted module. When restricting ourselves to the moonshine module, we obtain a new and conceptual proof that the moonshine module has a natural structure of a vertex operator algebra. This abelian intertwining algebra also contains an irreducible twisted module for the moonshine module with respect to the obvious involution. In addition, it contains a vertex operator superalgebra and a twisted module for this vertex operator superalgebra with respect to the involution which is the identity on the even subspace and is $-1$ on the odd subspace. It also gives the superconformal structures observed by Dixon, Ginsparg and Harvey.
26 pages. Final version to appear in the Proceedings of the Moonshine, the Monster, and related topics, Summer Research Conference, Mount Holyoke, 1994, Contemporary Mathematics
26 pages. Final version to appear in the Proceedings of the Moonshine, the Monster, and related topics, Summer Research Conference, Mount Holyoke, 1994, Contemporary Mathematics