On the Uniqueness of the Moonshine Vertex Operator Algebra
نویسندگان
چکیده
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 Griess algebra. Our two main theorems therefore establish a weak version of the FLM uniqueness conjecture for the moonshine vertex operator algebra. We believe that these are the first such results.
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