Related papers: Some finite properties for vertex operator superal…

For every $m \in {\C} \setminus \{0, -2\}$ and every nonnegative integer $k$ we define the vertex operator (super)algebra $D_{m,k}$ having two generators and rank $ \frac{3 m}{m + 2}$. If $m$ is a positive integer then $D_{m,k}$ can be…

This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard…

We examine the question of when, and how, the norm of a vector functional on an operator algebra can be controlled by the invariant subspace lattice of the algebra. We introduce a related operator algebraic property, and show that it is…

The radical of a vertex operator algebra associated to a module is defined and computed.

We give a natural extension of the notion of the contragredient module for a vertex operator algebra. By using this extension we prove that for regular vertex operator algebras, Zhu's $C_{2}$-finiteness condition holds, fusion rules are…

We provide a complete classification of unitary subalgebras of even rank-one lattice vertex operator algebras. As a consequence of the correspondence between vertex operator algebras and conformal nets, we also obtain a complete…

The vertex operator algebra structure of a strongly regular holomorphic vertex operator algebra $V$ of central charge $24$ is proved to be uniquely determined by the Lie algebra structure of its weight one space $V_1$ if $V_1$ is a Lie…

We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the…

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…

Let L be a Lie pseudoalgebra, a in L. We show that, if a generates a (finite) solvable subalgebra S=<a>, then one may find a lifting a' in S of [a] in S/S' such that <a'> is nilpotent. We then apply this result towards vertex algebras: we…

In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible…

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…

The new general upper bound mu <= [c/24] + 1 for the minimal weight mu of a self-dual vertex operator superalgebra of central charge c different from 47/2 is proven. For central charges c <= 48, further improved estimates are given and…

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.

We classify the irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to a positive definite even lattice of rank 1 under the automorphism lifted from the -1 isometry of L.

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 be a rank one positive definite even lattice. We prove that a vertex operator algebra (VOA) V_L^+ satisfies the C_2 condition. Here, V_L^+ is a fixed point sub-VOA of the VOA V_L associated with the automorphism lifted from the -1…

Let V be a vertex operator algebra and m,n be nonnegative integers. We construct an A_n(V)-A_m(V)-bimodule A_{n,m}(V) which determines the action of V from the level m subspace to level n subspace of an admissible V-module. We show how to…

We examine two nonselfadjoint operator algebras: the weighted shift algebra, and the Volterra operator algebra. In both cases, the operator algebra is the norm closure of the polynomials in the operator norm. In the case of the weighted…