Related papers: Orbifold Vertex Operator Algebras and the Positivi…

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

We prove that all holomorphic vertex operator algebras of central charge $24$ with non-trivial weight one subspaces are unitary. The main method is to use the orbifold construction of a holomorphic VOA $V$ of central charge $24$ directly…

We construct a class of non-weight modules over the twisted $N=2$ superconformal algebra $\T$. Let $\mathfrak{h}=\C L_0\oplus\C G_0$ be the Cartan subalgebra of $\T$, and let $\mathfrak{t}=\C L_0$ be the Cartan subalgebra of even part…

The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper we consider the general set-up of a vertex algebra $V$, graded by $\G/\Z$ for some…

Let $V$ be a vertex operator algebra and $g=\left(1\ 2\ \cdots k\right)$ be a $k$-cycle which is viewed as an automorphism of the vertex operator algebra $V^{\otimes k}$. It is proved that Dong-Li-Mason's associated associative algebra…

We extend the Dong-Mason theorem on the irreducibility of modules for orbifold vertex algebras from [C. Dong, G. Mason, Duke Math. J. 86 (1997)] 305-321] for the category of weak modules. Let $V$ be a vertex operator algebra, $g$ an…

In this paper, the irreducible modules for the $\mathbb{Z}_{2}$-orbifold vertex operator subalgebra of the parafermion vertex operator algebra associated to the irreducible highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$…

Let $V$ be a vertex operator superalgebra with the natural order 2 automorphism $\sigma$. Under suitable conditions on $V$, the $\sigma$-fixed subspace $V_{\bar 0}$ is a vertex operator algebra and the category $C_{V_{\bar 0}}$ of $V_{\bar…

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…

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

Let $V$ be a vertex operator subalgebra of $U$. Assume that $U$, $V$, and its commutant $V^c$ in $U$ are CFT-type, self-dual, and regular VOAs. Assume also that the double commutant $V^{cc}$ equals $V$. We prove that any intertwining…

We study the structure of operator algebras associated with the foliations which have projectively invariant measures. When a certain ergodicity condition on the measure preserving holonomies holds, the lack of holonomy invariant transverse…

In this article, we construct three new holomorphic vertex operator algebras of central charge $24$ using the $\mathbb{Z}_2$-orbifold construction associated to inner automorphisms. Their weight one subspaces has the Lie algebra structures…

In this article, we define operator algebras internal to a rigid C*-tensor category $\mathcal{C}$. A C*/W*-algebra object in $\mathcal{C}$ is an algebra object $\mathbf{A}$ in $\operatorname{ind}$-$\mathcal{C}$ whose category of free…

If a vertex operator algebra $V=\oplus_{n=0}^{\infty}V_n$ satisfies $\dim V_0=1, V_1=0$, then $V_2$ has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative)…

We classify vertex operator algebras (VOAs) of OZ-type generated by Ising vectors of $\sigma$-type. As a consequence of the classification, we also prove that such VOAs are simple, rational, $C_2$-cofinite and unitary, that is, they have…

In a recent paper [15], Hilbert space operators $T$ with the property that each sequence of the form $\{\|T^n h\|^2\}_{n=0}^{\infty}$ is conditionally positive definite in a semigroup sense were introduced. In the present paper, this line…

Representations of vertex operator algebras $V$ (VOAs) have numerous applications, including the construction of sheaves of conformal blocks on moduli spaces of curves. For a $V$-module $W = \oplus W_d$, a sequence of associative algebras…

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.

This paper is about the orbifold theory of affine vertex operator superalgebras. Among the main results, we classify the irreducible modules and determine the fusion rules for the orbifold of the simple affine vertex operator superalgebra…