Quantum vertex $C((t))$-algebras and quantum affine algebras (2009)
We give a summary of the theory of (weak) quantum vertex $\C((t))$-algebras and the association of quantum affine algebras with (weak) quantum vertex $\C((t))$-algebras.
Quantum vertex algebras and their phi-coordinated quasi modules (2009)
We introduce a notion of $\phi$-coordinated (quasi) module for a nonlocal vertex algebra and we establish a conceptual construction of nonlocal vertex algebras and their $\phi$-coordinated (quasi)...
Quantum vertex $F((t))$-algebras and their modules (2009)
This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, on the basis of \cite{li-qva1} we...
On quantum vertex algebras and their modules (2009)
We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double...
$\hbar$-adic quantum vertex algebras and their modules (2008)
This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we study notions of $\hbar$-adic...
Twisted modules for quantum vertex algebras (2008)
Li, Haisheng, Tan, Shaobin, Wang, Qing
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and...
On vertex algebras and their modules associated with even lattices (2008)
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new...
Some quantum vertex algebras of Zamolodchikov-Faddeev type (2008)
This is a continuation of a previous study of quantum vertex algebras of Zamolodchikov-Faddeev type. In this paper, we focus our attention on the special case associated to diagonal unitary rational...
VERTEX OPERATOR ALGEBRAS AND ASSOCIATIVE ALGEBRAS (2007)
Chongying Dong, Haisheng Li, Geoffrey Mason
Abstract. Let V be a vertex operator algebra. We construct a sequence of associative
Modules-at-infinity for quantum vertex algebras (2007)
This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we...
We continue a previous study on $\Gamma$-vertex algebras and their quasimodules. In this paper we refine certain known results and we prove that for any $\Z$-graded vertex algebra $V$ and a positive...
Twisted modules and quasi-modules for vertex operator algebras (2006)
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...
A smash product construction of nonlocal vertex algebras (2005)
A notion of vertex bialgebra and a notion of module nonlocal vertex algebra for a vertex bialgebra are studied and then a smash product construction of nonlocal vertex algebras is presented. For...
Constructing quantum vertex algebras (2005)
This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over $\C$, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of...
Cook, William J., Li, Haisheng, Misra, Kailash C.
Using certain results for the vertex operator algebras associated with affine Lie algebras we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an...
Twisted modules for vertex algebras associated with vertex algebroids (2005)
Li, Haisheng, Yamskulna, Gaywalee
We continue with [LY] to construct and classify graded simple twisted modules for the $\N$-graded vertex algebras constructed by Gorbounov, Malikov and Schechtman from vertex algebroids. Meanwhile we...
Pseudoderivations, pseudoautomorphisms and simple current modules for vertex algebras (2005)
We exhibit a connection between Etingof-Kazhdan's notion of pseudoderivation and a certain construction of simple current modules for a vertex operator algebra and meanwhile we introduce and study a...
Nonlocal vertex algebras generated by formal vertex operators (2005)
This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation...
On certain vertex algebras and their modules associated with vertex algebroids (2004)
Li, Haisheng, Yamskulna, Gaywalee
We study the family of vertex algebras associated with vertex algebroids, constructed by Gorbounov, Malikov, and Schechtman. As the main result, we classify all the (graded) simple modules for such...
Huang, Yi-Zhi, Lepowsky, James, Li, Haisheng, Zhang, Lin
We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a...
Abelianizing vertex algebras (2004)
To every vertex algebra $V$ we associate a canonical decreasing sequence of subspaces and prove that the associated graded vector space $gr(V)$ is naturally a vertex Poisson algebra, in particular a...
A new construction of vertex algebras and quasi modules for vertex algebras (2004)
In this paper, a new construction of vertex algebras from more general vertex operators is given and a notion of quasi module for vertex algebras is introduced and studied. More specifically, a...
On certain categories of modules for affine Lie algebras (2003)
In this paper, we re-examine certain integrable modules of Chari-Presslely for an (untwisted) affine Lie algebra $\hat{\g}$ by exploiting basic formal variable techniques. We define and study two...
Vertex algebras and vertex Poisson algebras (2002)
This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson...
Axiomatic $G_{1}$-vertex algebras (2002)
Inspired by the Borcherds' work on ``$G$-vertex algebras,'' we formulate and study an axiomatic counterpart of Borcherds' notion of $G$-vertex algebra for the simplest nontrivial elementary vertex...
Simple vertex operator algebras are nondegenerate (2002)
In this paper it is shown that every irreducible vertex algebra of countable dimension and every simple vertex operator algebra are nondegenerate in the sense of Etingof and Kazhdan.
On certain higher dimensional analogues of vertex algebras (2001)
A higher dimensional analogue of the notion of vertex algebra is formulated in terms of formal variable language with Borcherds' notion of $G$-vertex algebra as a motivation. Some examples are given...
Regular representations and Huang-Lepowsky's tensor functors for vertex operator algebras (2001)
This is the second paper in a series to study regular representations for vertex operator algebras. In this paper, given a module $W$ for a vertex operator algebra $V$, we construct, out of the dual...
Characterization of the cells in the knee joint meniscus / (2001)
Thesis (Ph. D.)--Cleveland State University, 2001.
On abelian generalized vertex algebras (2000)
This paper studies the algebraic aspect of a general abelian coset theory with a work of Dong and Lepowsky as our main motivation. It is proved that the vacuum space $\Omega_{V}$ (or the space of...
Generalized vertex algebras generated by parafermion-like vertex operators (2000)
It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural...
The regular representations and the $A_{n}(V)$ algebras (2000)
For a vertex operator algebra $V$, the regular representations are related to the $A_{n}(V)$-algebras and their bimodules, and induced $V$-modules from $A_{n}(V)$-modules are defined and studied in...
Certain extensions of vertex operator algebras of affine type (2000)
We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras $A_{k}(sl(2))$ for other types of simple Lie algebras. For all the constructed extended vertex operator...
The regular representation, Zhu's $A(V)$-theory and induced modules (1999)
The regular representation is related to Zhu's $A(V)$-theory and an induced module from an $A(V)$-module to a $V$-module is defined in terms of the regular representation. As an application, a new...
Regular representations of vertex operator algebras, I (1999)
In this paper, given a module $W$ for a vertex operator algebra $V$ and a nonzero complex number $z$ we construct a canonical (weak) $V\otimes V$-module ${\cal{D}}_{P(z)}(W)$ (a subspace of $W^{*}$...
On Z-graded associative algebras and their N-graded modules (1999)
Let $A$ be a $Z$-graded associative algebra and let $\rho$ be an irreducible $N$-graded representation of $A$ on $W$ with finite-dimensional homogeneous subspaces. Then it is proved that...
Certain generating subspaces for vertex operator algebras (1998)
We study minimal generating subspaces of "weak PBW type" for vertex operator algebras that satisfy a certain condition on the grading, and we develop a procedure for finding such subspaces. As...
Some finiteness properties of regular vertex operator algebras (1998)
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...
An analogue of the Hom functor and a generalized nuclear democracy theorem (1997)
We give an analogue of the Hom functor and prove a generalized form of the nuclear democracy theorem of Tsuchiya and Kanie by using a notion of tensor product for two modules for a vertex operator...
Modular invariance of trace functions in orbifold theory (1997)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of rational orbifold conformal field theory, in other words the theory of rational vertex operator...
Vertex operator algebras and associative algebras (1996)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
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...
Compact automorphism groups of vertex operator algebras (1996)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
Let $V$ be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group $G$ of automorphisms. We establish a Schur-Weyl type duality between the unitary,...
Certain associative algebras similar to $U(sl_{2})$ and Zhu's algebra $A(V_{L})$ (1996)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
It is proved that Zhu's algebra for vertex operator algebra associated to a positive-definite even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of certain associative...
Hom functor and the associativity of tensor products of modules for vertex operator algebras (1996)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
We give a new, construction-free proof of the associativity of tensor product for modules for rational vertex operator algebras under certain convergence conditions.
Vertex operator algebras associated to admissible representations of $\hat{sl}_2$ (1995)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
The admissible modules for $\hat{sl}_2$ are studied from the point of view of vertex operator algebra. If $l$ is rational such that $l+2={p\over q}$ for some coprime positive integers $p\ge 2$ and...
Twisted representations of vertex operator algebras (1995)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a...
Regularity of rational vertex operator algebras (1995)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
A regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient...
The theory of physical superselection sectors in terms of vertex operator algebra language (1995)
We formulate an interpretation of the theory of physical superselection sectors in terms of vertex operator algebra language. Using this formulation we give a construction of simple current from a...
Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules (1995)
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]....
Introduction to vertex operator algebras II (1995)
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...
Some twisted sectors for the Moonshine Module (1995)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
For the moonshine module $V^{\natural},$ whose automorphism is the Monster ${\Bbb M},$ We show how to give a uniform existence proof for irreducible $g$-twisted modules for elements of type $2A,$...
Simple currents and extensions of vertex operator algebras (1995)
Dong, Chongying, Li, Haisheng, Mason, Geoffrey
We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are {\em simple currents} associated with semisimple weight one...
Representation theory and tensor product theory for vertex operator algebras / (1994)
"Graduate Program in Mathematics."