Related papers: Representations of Vertex Operator Algebras $V_{L_…

The rationality and C_2-cofiniteness of the orbifold vertex operator algebra V_{L_{2}}^{A_{4}} are established and all the irreducible modules are constructed and classified. This is part of classification of rational vertex operator…

The rational vertex operator algebra $V_{L_{2}}^{A_{4}}$ is characterized in terms of weights of primary vectors. This reduces the classification of rational vertex operator algebras with $c=1$ to the characterizations of…

We demonstrate that, for CFT vertex operator algebras, C_2-cofiniteness and rationality is equivalent to regularity. In addition, we show that, for C_2-cofinite vertex operators algebras, irreducible weak modules are ordinary modules and…

A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible…

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras A_n(V) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is…

For a vertex operator algebra V, a V-module M and a nonnegative integer n, an A_n(V)-bimodule A_n(M) is constructed and studied. The connection between A_n(M) and intertwining operators are discussed. In the case that V is rational, A_n(M)…

The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The irreducible modules of vertex operator algebra…

It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.

Let $A$ be a finite dimensional unital commutative associative algebra and let $B$ be a finite dimensional vertex $A$-algebroid such that its Levi factor is isomorphic to $sl_2$. Under suitable conditions, we construct an indecomposable…

The rationality of the parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra and any nonnegative integer is established and the irreducible modules are determined.

We show that C_2-cofiniteness is enough to prove a modular invariance property of vertex operator algebras without assuming the semisimplicity of Zhu algebra. For example, if a VOA V=\oplus_{m=0}^{\infty}V_m is C_2-cofinite, then the space…

Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is…

We investigate vertex operator algebras $L(k,0)$ associated with modular-invariant representations for an affine Lie algebra $A_1 ^{(1)}$ , where k is 'admissible' rational number. We show that VOA $L(k,0)$ is rational in the category $\cal…

Let L_{B}(-5/2,0) (resp. L_{F}(-5/2,0)) be the simple vertex operator algebra associated to affine Lie algebra of type $B_{4}^{(1)}$ (resp. $F_{4}^{(1)}$) with the lowest admissible half-integer level -5/2. We show that L_{B}(-5/2,0) is a…

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

The admissible modules for $\hat{sl}_2$ are studied from the point of view of vertex operator algebra. If $l$ is rational such that $l+2={p\over q}$ for some coprime positive integers $p\ge 2$ and $q$, Kac and Wakimoto found finitely many…

It was shown by Abe, Buhl and Dong that the vertex algebra $V_L^+$ and its irreducible weak modules satisfy the $C_2$-cofiniteness condition when $L$ is a positive definite even lattice. In this paper, we extend their results by showing…

The irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to an arbitrary positive definite even lattice L under the automorphism lifted from the -1 isometry of L are…

In this paper, under the assumption that the diagonal coset vertex operator algebra $C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak g}(l,0))$ is rational and $C_2$-cofinite, the global dimension of $C(L_{\mathfrak…

In this paper, it is shown that the diagonal coset vertex operator algebra $C(L_{\mathfrak{g}}(k+2,0),L_{\mathfrak{g}}(k,0)\otimes L_{\mathfrak{g}}(2,0))$ is rational and $C_2$-cofinite in case $\mathfrak{g}=so(2n), n\geq 3$ and $k$ is an…