Abstract
Given a commutative associative algebra A with an associative form (’), we construct a vertex operator algebra V with the weight two space V2;≅ A If in addition the form (’) is nondegenerate, we show that there is a simple vertex operator algebra with V2;≅ A We also show that if A is semisimple, then the vertex operator algebra constructed is the tensor products of a certain number of Virasoro vertex operator algebras.
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