Related papers: Vertex operator algebras generated by Ising vector…
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 this paper, we study a class of simple OZ-type vertex operator algebras $V$ generated by simple Virasoro vectors $\omega^{ij}=\omega^{ji}$, $1\leq i<j\leq n$, $n\geq 3$. We prove that $V$ is uniquely determined by its Griess algebra…
Let $r \in \BC$ be a complex number, and $d \in \BZ_{\ge 2}$ a positive integer greater than or equal to 2. Ashihara and Miyamoto introduced a vertex operator algebra $\Vam$ of central charge $dr$, whose Griess algebra is isomorphic to the…
A series of vertex operator algebras are constructed by GKO-construction, which is a generalization of 3A-algebra and 6A-algebra. It is proved their vertex operator algebra structures are unique under nonzero assumptions on some elements of…
In this article, we study Griess algebras and vertex operator subalgebras generated by Ising vectors in a moonshine type VOA such that the subgroup generated by the corresponding Miyamoto involutions has the shape $3^2{:}2$ and any two…
In this article, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors $I$ such that (1) for any $e\neq f\in I$, the subVOA $\mathrm{VOA}(e,f)$ generated by $e$ and $f$ is isomorphic to…
In this paper, we study the subalgebra generated by two Ising vectors in the Griess algebra of a vertex operator algebra. We show that the structure of it is uniquely determined by some inner products of Ising vectors. We prove that the…
Let $L$ be an even lattice without roots. In this article, we classify all Ising vectors in the vertex operator algebra $V_L^+$ associated with $L$.
In this paper we mainly study the vertex operator algebra $\mathbb{C} \mathrm{VA}(e, f)$ generated by two Ising vectors $e$ and $f$ with $\langle e, f\rangle=\frac{5}{2^{10}}$. We prove $\mathbb{C} \mathrm{VA}(e, f)$ is isomorphic to the…
In this article we study and obtain a classification of Ising vectors in vertex operator algebras associated to binary codes and $\sqrt{2}$ times root lattices, where an Ising vector is a conformal vector with central charge 1/2 generating…
It is proved that a vertex operator algebra is isomorphic to the moonshine VOA of Frenkel-Lepowsky-Meurman if it satisfies certain conditions. Our two main theorems establish a weak version of the FLM uniqueness conjecture for the moonshine…
In this paper we study a series of vertex operator algebras of integer level associated to the affine Lie algebra $A_{\ell}^{(1)}$. These vertex operator algebras are constructed by using the explicit construction of certain singular…
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that…
We describe an approach to classify (meromorphic) representations of a given vertex operator algebra by calculating Zhu's algebra explicitly. We demonstrate this for FKS lattice theories and subtheories corresponding to the Z_2 reflection…
Geometric vertex algebras are a simplified version of Huang's geometric vertex operator algebras. We give a self-contained account of the equivalence of geometric vertex algebras with Z-graded vertex algebras.
It is proved that any vertex operator algebra for which the image of the Virasoro element in Zhu's algebra is algebraic over complex numbers is finitely generated. In particular, any vertex operator algebra with a finite dimensional Zhu's…
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)…
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…
We give an abstract construction, based on the Belavin-Polyakov-Zamolodchikov equations, of a family of vertex operator algebras of rank $26$ associated to the modified regular representations of the Virasoro algebra. The vertex operators…
We formulate the basic properties of q-vertex operators in the context of the Andrews-Baxter-Forrester (ABF) series, as an example of face-interaction models, derive the q-difference equations satisfied by their correlation functions, and…