Ternary Codes and Vertex Operator Algebras

Vertex operator algebras have been studied from a wide variety of view point. This implies rich properties of vertex operator algebras. Recently investigation of vertex operator algebras as modules for their subalgebras n Ž . isomorphic to a tensor product m L c , 0 of Virasoro vertex operator i is1 w x algebras was initiated by Dong et al. DMZ . Along this line Miyamoto w x M2 constructed a series of vertex operator algebras by combining the 1 1 1 Ž . Ž . minimal vertex operator super algebra L , 0 [ L , with even binary 2 2 2 codes. In this article we construct vertex operator algebras associated with self ' Ž . orthogonal ternary codes. We begin with a lattice L s 2 A -lattice . It is 2 w x known DLMN that the vertex operator algebra V contains a subalgebra L 1 7 4 Ž . Ž . Ž . T isomorphic to L , 0 m L , 0 m L , 0 . Inspecting the action of T 2 10 5 4 4 Ž . Ž . we obtain a vertex operator algebra isomorphic to L , 0 [ L , 3 and 5 5 4 2 Ž . two of its modules, both of which is isomorphic to L , . Combining 5 3

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