Related papers: Integral forms in vertex operator algebras, a surv…
This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…
We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the $W$ algebra defined using nilpotent orbit with partition $[q^m,1^s]$. Gauging above AD…
We generalize the notion of an intertwining operator to N-graded weak modules over a vertex operator algebra and study their properties. We show a formula for the dimensions of these intertwining operators in terms of modules over the Zhu…
In this article, we describe how coalgebraic structures on operads induce algebraic structures on their categories of algebras and coalgebras.
In this article, we study module categries of simple current extensions of vertex operator algebras. Under certain assumptions, we show that every module for a rational vertex operator algebra be lifted to a twisted module for an extended…
The energy bounds condition for intertwining operators of unitary rational vertex operator algebras (VOAs) was studied, first by A.Wassermann for type $A$ affine VOAs, and later by T.Loke for $c<1$ Virasoro VOAs, and by V.Toledano-Laredo…
We construct bosonized vertex operators (VOs) and conjugate vertex operators (CVOs) of $U_q(su(2)_k)$ for arbitrary level $k$ and representation $j\leq k/2$. Both are obtained directly as two solutions of the defining condition of vertex…
We study a special class of holomorphic vertex operator algebras (VOAs) that we call \emph{balanced}.\ For a balanced, holomorphic VOA $V=\mathbb{C}\mathbf{1}\oplus V_1\oplus\dots$ with $c=32$ or $40$ we show that the Virasoro vectors of…
For a vertex operator algebra V, a V-module M and a nonnegative integer n, an A_n(V)-bimodule A_n(M) is constructed and studied. The connection between A_n(M) and intertwining operators are discussed. In the case that V is rational, A_n(M)…
We review definitions and basic properties of operads, PROPs and algebras over these structures.
We propose a classical analogue of the vertex algebra in the context of classical integrable field theories. We use this fundamental notion to describe the auxiliary function of the linear auxiliary problem as a classical vertex operator.…
A multiple operator integral (MOI) is an indispensable tool in several branches of noncommutative analysis. However, there are substantial technical issues with the existing literature on the "separation of variables" approach to defining…
Circuit algebras are a symmetric analogue of Jones's planar algebras introduced to study finite-type invariants of virtual knotted objects. Circuit algebra structures appear, in different forms, across mathematics. This paper provides a…
Let $V_1 \otimes V_2$ be a tensor product of VOAs. Using Zhu theory we discuss the theory of representations of V (associative algebra, modules and fusion rules). We prove that this theory is more or less the same as representation theory…
In this paper, we introduce a new induction functor $\mathrm{Ind}^V_U$ between module categories corresponding to an embedding of vertex operator algebras (VOAs) $U \hookrightarrow V$. This induction functor is essentially defined at the…
In this paper, mirror extensions of vertex operator algebras is considered via tensor categories. The mirror extension conjecture is proved.
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
We construct some inverse-closed algebras of bounded integral operators with operator-valued kernels, acting in spaces of vector-valued functions on locally compact groups. To this end we make systematic use of covariance algebras…
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…
Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies the role played by the integral counterpart of the…