Related papers: Twisted Modules over Vertex Algebras on Algebraic …
In this paper, we show that the tilting modules over a cluster-tilted algebra $A$ lift to tilting objects in the associated cluster category $\mathcal{C}_H$. As a first application, we describe the induced exchange relation for tilting…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
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.
This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m,n in (1/T)Z_+, an A_{g,n}(V)-A_{g,m}(V)-bimodule A_{g,n,m}(V) is…
We introduce and study twisted triangular Banach algebras T_sigma(A,B;X), built from Banach algebras A,B, a Banach A-B bimodule X, and a pair of automorphisms sigma=(sigma_A,sigma_B). This construction extends the classical triangular…
A module M over a vertex algebra V is half-integrable if a_n act locally nilpotently on M for all a in V, m in M, n>0. We study half-integrable modules over sheaves of twisted chiral differential operators (TCDO) on a smooth variety X. We…
Given a field $K$ and an ample (not necessarily Hausdorff) groupoid $G$, we define the concept of a line bundle over $G$ inspired by the well known concept from the theory of C*-algebras. If $E$ is such a line bundle, we construct the…
Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line…
Suppose that a finite group $G$ acts on a smooth complex variety $X$. Then this action lifts to the Chiral de Rham Complex of $X$ and to its cohomology by automorphisms of the vertex algebra structure. We define twisted sectors for the…
We consider the Etingof-Kazhdan quantum vertex algebra $\mathcal{V}^c(\mathfrak{gl}_N)$ associated with the trigonometric $R$-matrix of type $A$. By combining Li's theory of $\phi$-coordinated modules and the ideas from our previous paper,…
We construct twisting functors for quantum group modules. First over the field $\mathbb{Q}(v)$ but later over any $\mathbb{Z} [v,v^{-1}]$-algebra. The main results in this paper are a rigerous definition of these functors, a proof that they…
We define and study twisted support varieties for modules over an Artin algebra, where the twist is induced by an automorphism of the algebra. Under a certain finite generation hypothesis, we show that the twisted variety of a module…
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 results are obtained. We also study…
We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally…
We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…
We investigate a question posed by Gaberdiel and Gannon concerning the relationship between $C_{2}$-algebras and twisted modules. To each twisted module $W$ of a vertex algebra $V$, we first associate a decreasing sequence of subspaces…
Every isometry $\sigma$ of a positive-definite even lattice $Q$ can be lifted to an automorphism of the lattice vertex algebra $V_Q$. An important problem in vertex algebra theory and conformal field theory is to classify the…
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…
Given a smooth compact complex surface together with a holomorphic line bundle on it, using the theory of Hodge modules, we compute the twisted Hodge groups/numbers of Hilbert schemes (or Douady spaces) of points on the surface with values…
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…