Related papers: Integral forms in vertex operator algebras, a surv…

For a vertex operator algebra $V$ with conformal vector $\omega$, we consider a class of vertex operator subalgebras and their conformal vectors. They are called semi-conformal vertex operator subalgebras and semi-conformal vectors of…

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…

We consider the algebraic structure of $\mathbb{N}$-graded vertex operator algebras with conformal grading $V=\oplus_{n\geq 0} V_n$ and $\dim V_0\geq 1$. We prove several results along the lines that the vertex operators $Y(a, z)$ for $a$…

The direct sum of irreducible level one integrable representations of affine Kac-Moody Lie algebra of (affine) type $ADE$ carries a structure of $P/Q$-graded vertex operator algebra. There exists a filtration on this direct sum studied by…

A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…

We give a representation--theoretic interpretation of recent discovered coupled soliton equations using vertex operators construction of affinization of not simple but quadratic Lie algebras. In this setup we are able to obtain new…

This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.

We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show…

This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.

We announce a new type of "Jacobi identity" for vertex operator algebras, incorporating values of the Riemann zeta function at negative integers. Using this we "explain" and generalize some recent work of S. Bloch's relating values of the…

We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity and operator product expansions are formulated and proved. We also give…

We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…

We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…

This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schroedinger operators.

This is the first 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…

We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…

In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…

We construct orbifolds of holomorphic lattice Vertex Operator Algebras for non-Abelian finite automorphism groups $G$. To this end, we construct twisted modules for automorphisms $g$ together with the projective representation of the…

We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…