Vertex operator algebras with positive central charges whose dimensions of weight one spaces are 8 and 16

摘要

We classify rational simple self-dual vertex operator algebras V of CFT and of finite type with positive central charges, where dV = dim V1 is either 8 or 16, under the condition that the space spanned by characters of V -modules is equal to the solution space of some monic modular linear differential equation of the third order. It is shown that central charges are c = 8 for dV = 8, and c = 4, 16 for dim dV = 16, respectively. In fact, under the condition that V1 equipped with the 0th product of V are abelian Lie algebras for dV = 8, c = 8 and dV = 16, c = 16, the vertex operator algebras V are isomorphic to V root 2E8 and V Lambda 16, respectively. For dV = 16 and c = 4, V is isomorphic to the lattice vertex operator algebra VA2 circle plus A2 .

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