Related papers: Rationality, Regularity, and C_2-cofiniteness

We first investigate the algebraic structure of vertex algebroids $B$ when $B$ are simple Leibniz algebras. Next, we use these vertex algebroids $B$ to construct indecomposable non-simple $C_2$-cofinite $\mathbb{N}$-graded vertex algebras…

We construct a family of potentially quasi-lisse (non-rational) vertex algebras, denoted by $\mathcal{C}_p$, $p \geq 2$, which are closely related to the vertex algebra of chiral differential operators on $SL(2)$ at level $-2+\frac{1}{p}$.…

We discuss our recent results on the representation theory of $\mathcal{W}$--algebras relevant to Logarithmic Conformal Field Theory. First we explain some general constructions of $\mathcal{W}$-algebras coming from screening operators.…

Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is…

We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…

Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is…

This paper consists of two parts: (1) Using a Z[1/2]-form of Virasoro vertex operator algebra L(1/2,0) with central charge 1/2, we obtain a modular vertex operator algebra over any field F of finite characteristic different from 2. We…

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…

Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…

Let $V$ be a simple VOA of CFT-type satisfying $V'\cong V$ and $\sigma$ a finite automorphism of $V$. We prove that if all $V$-modules are completely reducible and a fixed point subVOA $V^\sigma$ is $C_2$-cofinite, then all…

We prove the rationality of all the minimal series principal W-algebras discovered by Frenkel, Kac and Wakimoto in 1992, thereby giving a new family of rational and C_2-cofinite vertex operator algebras. A key ingredient in our proof is the…

The irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to an arbitrary positive definite even lattice L under the automorphism lifted from the -1 isometry of L are…

For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$ of $\hat{\mathfrak{g}}$, we prove that certain subcategory of weak $V_k(\mathfrak{g})$-module category is semisimple. As a consequence, we show that…

First, we establish the relation between the associated varieties of modules over Kac-Moody algebras \hat{g} and those over affine W-algebras. Second, we prove the Feigin-Frenkel conjecture on the singular supports of G-integrable…

We develop a spanning set for weak modules of C_2 co-finite vertex operator algebras. This spanning set has finiteness properties that we use to show weak modules are C_n co-finite and A_n(M) is finite dimensional.

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 $\mathbb V=\bigoplus_{n\in\mathbb N}\mathbb V(n)$ be a $C_2$-cofinite VOA, not necessarily rational or self-dual. In this paper, we establish various versions of the sewing-factorization (SF) theorems for conformal blocks associated to…

We give an algebraic proof of the unitarity of the vertex operator algebra $L(21/22, 0)\oplus L(21/22, 8)$ and of all its irreducible ordinary modules, using a coset realization arising from the $3C$-algebra. Motivated by the structure of…

Let V be a vertex operator algebra. We construct a sequence of associative algebras A_n(V) (n=0,1,2,...) such that A_{n}(V) is a quotient of A_{n+1}(V) and a pair of functors between the category of A_n(V)-modules which are not…

This is a survey of some results on the structure and classification of normal analytic compactifications of C^2. Mirroring the existing literature, we especially emphasize the compactifications for which the curve at infinity is…