Construction of vertex operator algebras from commutative associative algebras

@article{Lam1996ConstructionOV,
  title={Construction of vertex operator algebras from commutative associative algebras},
  author={Ching Hung Lam},
  journal={Communications in Algebra},
  year={1996},
  volume={24},
  pages={4339-4360}
}
  • C. Lam
  • Published 1996
  • Mathematics
  • Communications in Algebra
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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Abstract In this paper, we construct a family of vertex operator algebras parameterized by a non-zero complex number r, whose Griess algebras V2 are isomorphic to Hermitian Jordan algebras of type C…
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For a given simple Jordan algebra A of type A, B or C over C, we construct a vertex operator algebra V such that the weight two space V 2 ≅ A by using the structure of Heisenberg algebras. In…
Simplicity of a Vertex Operator Algebra Whose Griess Algebra is the Jordan Algebra of Symmetric Matrices
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On a family of vertex operator superalgebras
ϕϵ-Coordinated modules for vertex algebras
2 2 Ja n 19 99 Vertex algebras generated by Lie algebras
In this paper we introduce a notion of vertex Lie algebra U , in a way a “half” of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U).…
On Correlation Functions of Vertex Operator Algebras Associated to Jordan Algebras
Lie Conformal Algebra and Dual Pair Type Realizations of Some Moonshine Type VOAs, and Calculations of the Correlation Functions
In this paper we use Lie conformal algebras to realize some moonshine type VOAs, whose Greiss algebras are Jordan algebras. On the other hand, we consider some free fields which realizes the…
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