Related papers: Bimodules associated to vertex operator algebras

We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…

We determine the level two Zhu algebra for the Heisenberg vertex operator algebra $V$ for any choice of conformal element. We do this using only the following information for $V$: the internal structure of $V$; the level one Zhu algebra of…

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice…

By using generalized vertex algebras associated to rational lattices, we construct explicitly the admissible modules for the affine Lie algebra $A_1 ^{(1)}$ of level $-{4/3}$. As an application, we show that the W(2,5) algebra with central…

In this paper, we shall give a way to construct a graded Lie algebra $L(\mathfrak{g},\rho,V,{\cal V},B_0)$ from a standard pentad $(\mathfrak{g},\rho,V,{\cal V},B_0)$ which consists of a Lie algebra $\mathfrak{g}$ which has a non-degenerate…

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

Given an Archimedean order unit space (V,V^+,e), we construct a minimal operator system OMIN(V) and a maximal operator system OMAX(V), which are the analogues of the minimal and maximal operator spaces of a normed space. We develop some of…

Given a weight-one element $u$ of a vertex operator algebra $V$, we construct an automorphism of the category of generalized $g$-twisted modules for automorphisms $g$ of $V$ fixing $u$. We apply this construction to the case that $V$ is an…

For a vertex operator algebra $V$ and a vertex operator subalgebra $V'$ which is invarinant under an automorphism $g$ of $V$ of finite order, we introduce a $g$-twisted induction functor from the category of $g$-twisted $V'$-modules to the…

Let $V$ be a vertex operator superalgebra and $g=\left(1\ 2\ \cdots k\right)$ be a $k$-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra $V^{\otimes k}$. In this paper, we construct an explicit…

We introduce the notion of ``local system of $\Bbb{Z}_{T}$-twisted vertex operators'' on a $\Bbb{Z}_{2}$-graded vector space $M$, generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of…

An averaging operator on an associative algebra $A$ is an algebraic abstraction of the time average operator on the space of real-valued functions defined in time-space. In this paper, we consider relative averaging operators on a bimodule…

Let $V$ be a simple vertex algebra of countable dimension, $G$ be a finite automorphism group of $V$ and $\sigma$ be a central element of $G$. Assume that ${\cal S}$ is a finite set of inequivalent irreducible $\sigma$-twisted $V$-modules…

We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…

The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…

The set of normalizers between von Neumann (or, more generally, reflexive) algebras A and B, (that is, the set of all operators x such that xAx* is a subset of B and x*Bx is a subset of A) possesses `local linear structure': it is a union…

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…

This paper is to study vertex operator superalgebras which are strongly generated by their weight-$2$ and weight-$\frac{3}{2}$ homogeneous subspaces. Among the main results, it is proved that if such a vertex operator superalgebra $V$ is…

Let $G$ be a simple complex Lie group with Lie algebra $\mf g$ and let $\af$ be the affine Lie algebra. We use intertwining operators and Knizhnik-Zamolodchikov equations to construct a family of $\N$-graded vertex operator algebras…

It is proved that g-rationality of a vertex operator superalgebra V=V_{\bar0}+V_{\bar1} for all g in G imply rationality of V^G, and also imply that each irreducible V^G-module is a submodule of an irreducible g-twisted V-module for some g…