Construction of vertex operator algebras from commutative associative algebras

  title={Construction of vertex operator algebras from commutative associative algebras},
  author={Ching Hung Lam},
  journal={Communications in Algebra},
  • 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. 
On a VOA Associated with the Simple Jordan Algebra of Type D
If a vertex operator algebra satisfies dim V 0 = 1 and V 1 = {0}, then V 2 has a commutative (not necessarily associative) algebra structure, called the Griess algebra. By using a vertex operator
On vertex operator algebras associated to Jordan algebras of Hermitian type
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
On voa associated with special jordan algebras
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
Let r ∈ ℂ be a complex number, and d ∈ ℤ≥2 a positive integer greater than or equal to 2. Ashihara and Miyamoto [4] introduced a vertex operator algebra V 𝒥 of central charge dr, whose Griess
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).
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


Generalized vertex algebras and relative vertex operators
1. Introduction. 2. The setting. 3. Relative untwisted vertex operators. 4. Quotient vertex operators. 5. A Jacobi identity for relative untwisted vertex operators. 6. Generalized vertex operator
Vertex algebras, Kac-Moody algebras, and the Monster.
  • R. Borcherds
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1986
An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.
Vertex operator algebras associated to representations of affine and Virasoro Algebras
The first construction of the integrable highest-weight representations of affine Lie algebras or loop algebras by Kac i-K] was greatly inspired by the generalization of the Weyl denominator formula
On the classification of simple vertex operator algebras
Inspired by a recent work of Frenkel-Zhu, we study a class of (pre-)vertex operator algebras (voa) associated to the self-dual Lie algebras. Based on a few elementary structural results we propose
On Axiomatic Approaches to Vertex Operator Algebras and Modules
Introduction Vertex operator algebras Duality for vertex operator algebras Modules Duality for modules References.
On vertex operator algebras as sl 2 -modules
Suppose that V is a vertex operator algebra (VOA). One of the axioms for a VOA is that V is a module for the Virasoro algebra Vir, and in particular there are operators L(0), L(1), L(−1) in Vir which
The friendly giant