Related papers: Zhu's algebra, the C_2 algebra, and twisted module…
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…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
Vertex algebras (and their modules) can be described as vector spaces together with a linear operator-valued series in one parameter $z$. With the interpretation of $z$ as a coordinate at a point on a curve, one can construct algebraic…
Certain deformable families of vertex algebras acquire at a limit of the deformation parameter a large center, similar to affine Lie algebras at critical level. Then the vertex algebra and its representation category become a bundle over…
In recent work, Wang and the third author defined a class of 'extremal' vertex operator algebras (VOAs), consisting of those with at least two simple modules and conformal dimensions as large as possible for the central charge. In this…
We classify, up to isomorphism, twisted graded Calabi--Yau algebras of dimension two on two-vertex quivers. By work of Reyes and Rogalski, such algebras may be presented as quotients of translation quivers by mesh relations. We also…
We obtain the operator algebra of each twisted sector of all WZW orbifolds, including the general twisted current algebra and the algebra of the twisted currents with the twisted affine primary fields. Surprisingly, the twisted right and…
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 proof of Frenkel and Zhu's fusion rule…
A major open problem in the theory of twisted commutative algebras (tca's) is proving noetherianity of finitely generated tca's. For bounded tca's this is easy, in the unbounded case, noetherianity is only known for Sym(Sym^2(C^\infty)) and…
Given two algebras A and B, sometimes assumed to be C*-algebras, we consider the question of putting algebra or C*-algebra structures on the tensor product A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize all…
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…
In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related…
We obtain explicit formulas for the $1$-point functions of all states in the symmetrized Heisenberg algebra $M^+$ and symmetrized lattice VOAs $V_L^+$. For this we employ a new $\mathbf Z_2$-twisted variant of so-called Zhu recursion.
We introduce the notion of a computably strongly self-absorbing C*-algebra and show that the following C*-algebras are computably strongly self-absorbing: the Cuntz algebras $\mathcal{O}_2$ and $\mathcal{O}_\infty$, the UHF algebra…
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 introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let $V$ be a vertex operator algebra and let $g_{1}$, $g_{2}$…
We study the representation theory and enveloping $C^*$-algebras for Wick analogues of CAR and twisted CAR algebras. The realization of the $C^*$-algebras under consideration as algebras of continuous matrix-functions satisfying certain…
We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary…
We introduce two $K$-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these…
For a finitely-generated vertex operator algebra of central charge c, a locally convex topological completion is constructed. We construct on the completion a structure of an algebra over the operad of the c/2-th power of the determinant…