Uniqueness results for the moonshine vertex operator algebra
نویسندگان
چکیده
منابع مشابه
On the Uniqueness of the Moonshine Vertex Operator Algebra
It is proved that the vertex operator algebra V is isomorphic to the moonshine VOA V ♮ of Frenkel-Lepowsky-Meurman if it satisfies conditions (a,b,c,d) or (a,b,c,d). These conditions are: (a) V is the only irreducible module for itself and V is C2-cofinite; (a) dimVn ≤ dimV ♮ n for n ≥ 3; (b) the central charge is 24; (c) V1 = 0; (d) V2 (under the first product on V ) is isomorphic to the Gries...
متن کاملA construction of vertex operator algebra . I ( The moonshine VOA )
We study a simple vertex operator algebra (VOA) V containing a set of mutually orthogonal simple conformal vectors ei : i = 1, ..., n with central charge 12 such that the sum is the Virasoro element. In [M3], the author showed that it defines two mutually orthogonal binary linear codes D and S. We prove that V is the only irreducible V -module if D = S⊥. Applying the way of constructing VOA giv...
متن کاملA Nonmeromorphic Extension of the Moonshine Module Vertex Operator Algebra
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 oper...
متن کاملA Characterization of the Moonshine Vertex Operator Algebra by Means of Virasoro Frames
In this article, we show that a framed vertex operator algebra V satisfying the conditions: (1) V is holomorphic (i.e, V is the only irreducible V -module); (2) V is of rank 24; and (3) V1 = 0; is isomorphic to the moonshine vertex operator algebra V \ constructed by Frenkel-Lepowsky-Meurman [12].
متن کاملFramed vertex operator algebras, codes and the moonshine module
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 ...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2007
ISSN: 1080-6377
DOI: 10.1353/ajm.2007.0009