Related papers: Fusion rules for the vertex operator algebras M(1)…

We discuss a recent proof by the author of a general version of the Verlinde conjecture in the framework of vertex operator algebras and the application of this result to the construction of modular tensor tensor category structure on the…

A characterization of vertex operator algebra V_{Z\alpha}^+ with (\alpha,\alpha)/2 not being a perfect square is given in terms of dimensions of homogeneous subspaces of small weights. This result contributes to the classification of…

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…

The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.

We prove a determinant formula for the standard integral form of a lattice vertex operator algebra.

The initial classification of fusion rules have shown that rational conformal field theory is very limited. In this paper we study the fusion rules of extend ed current algebras. Explicit formulas are given for the S matrix and the fusion…

The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If the level satisfies a certain coprime property…

After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…

The vertex operator algebra M(1)^+ is the fixed point set of free bosonic vertex operator algebra M(1) under the -1 automorphism. All irreducible modules for M(1)^+ are classified in this paper for all ranks.

In this paper, we give a characterization of the rational vertex operator algebra VTL, where L is the root lattice of type A1 and T is the tetrahedral group.

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…

In this paper, irreducible modules of the diagonal coset vertex operator algebra $C(L_{\mathfrak{g}}(k+l,0),L_{\mathfrak{g}}(k,0)\otimes L_{\mathfrak{g}}(l,0))$ are classified under the assumption that…

We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which plays an important role in the classification of lattices. We derive a formula relating…

Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show…

We analyze the properties of the q-vertex operators of U_q(sl(2)^) introduced by Frenkel and Reshetikhin. As the condition for the null vector decoupling, we derive the existence condition of the q-vertex operators ( the fusion rules ).

The quantum dimensions and the fusion rules for the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k are determined.

For certain vertex operator algebras (e.g., lattice type) and given finite group of automorphisms, we prove existence of a positive definite integral form invariant under the group. Applications include an integral form in the Moonshine VOA…

Vertex operator superalgebras are studied and various results on rational Vertex operator superalgebras are obtained. In particular, the vertex operator super subalgebras generated by the weight 1/2 and weight 1 subspaces are determined. It…

Let $V$ be a vertex operator algebra equipped with two commuting finite-order automorphisms $g_1$ and $g_2$, and set $g_3 = g_1 g_2$. For $k = 1, 2, 3$, let $W^k$ be a $g_k$-twisted $V$-module. Assuming that $W^1$ and $W^2$ are…

Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V. We give two sufficient conditions implying that V is energy-bounded. The first condition is…