Related papers: Introduction to vertex operator algebras I
This is the third part of the revised versions of the notes of three consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi Huang in the conference on Monster and vertex operator algebras at the Research Institute…
This is the second part of the revised versions of the notes of three consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi Huang in the conference on Monster and vertex operator algebras at the Research Institute…
In this paper, we use the twisted regular representation theory of vertex operator algebras to construct bimodules over twisted Zhu algebras, extending Haisheng Li's work in untwisted scenarios. Moreover, a conjecture of Dong and Jiang on…
In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
We use a result of Barron, Dong and Mason to give a natural isomorphism between the category of twisted modules and the category of quasi-modules of a certain type for a general vertex operator algebra.
We give a new construction of functors from the category of modules for the associative algebras $A_n(V)$ and $A_g(V)$ associated with a vertex operator algebra $V$, defined by Dong, Li and Mason, to the category of admissible $V$-modules…
This contribution is mainly based on joint papers with Lepowsky and Milas, and some parts of these papers are reproduced here. These papers further extended works by Lepowsky and by Milas. Following our joint papers, I explain the general…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…
In this paper, we define differential graded vertex operator algebras and the algebraic structures on the associated Zhu algebras and $C_2$-algebras. We also introduce the corresponding notions of modules, and investigate the relations…
In his landmark paper, Zhu associated two associative algebras to a vertex operator algebra: what are now called Zhu's algebra and the C_2-algebra. The former has a nice interpretation in terms of the representation theory of the VOA, while…
In this paper, we study the algebra of twisted vertex operators over an even integral ${\mathbf Z}_2$-lattice, and give a kind of systematic construction of fundamental representations for affine Lie algebras of type $A$, $D$, $E$ with…
These are the lecture notes for a course taught at Tsinghua University in the spring of 2022. In these notes, we develop the basic theory of vertex operator algebras (VOAs) and their conformal blocks using complex-analytic methods. In…
Using recursion formulas for vertex operator algebra higher genus characters with formal parameters identified with local coordinates around marked points on a Riemann surface of arbitrary genus, we introduce the notion of a vertex operator…
This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In…
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…
This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices $L$ whose Gram matrix contains only non-negative…
Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules…
Motivated by the study of indecomposable, nonsimple modules for a vertex operator algebra $V$, we study the relationship between various types of $V$-modules and modules for the higher level Zhu algebras for $V$, denoted $A_n(V)$, for $n…