Related papers: Classification of transitive vertex algebroids
We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly…
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…
A VB-algebroid is a vector bundle object in the category of Lie algebroids. We attach to every VB-algebroid a differential graded Lie algebra and we show that it controls deformations of the VB-algebroid structure. Several examples and…
In this article, we investigate Hecke modifications of vector bundles on a smooth projective curve $X$ defined over an arbitrary field. We obtain structural results that allow us to reduce the classification problem of Hecke modifications…
Deformation quantization algebroids over a complex symplectic manifold X are locally given by rings of WKB operators, that is, microdifferential operators with an extra central parameter \tau. In this paper, we will show that such…
We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe…
We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show…
Let \(X\) be an irreducible smooth complex projective variety, and let \(G\) be a connected reductive linear algebraic group over \(\mathbb{C}\). In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We…
We describe a conjectural classification of Poisson vertex algebras of CFT type and of Poisson vertex algebras in one differential variable (= scalar Hamiltonian operators).
In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…
A vertex algebra with an action of a group $G$ comes with a notion of $g$-twisted modules, forming a $G$-crossed braided tensor category. For a Lie group $G$, one might instead wish for a notion of $(\mathrm{d}+A)$-twisted modules for any…
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 classify irreducible twisted modules for a…
Transitive Lie algebroids have specific properties that allow to look at the transitive Lie algebroid as an element of the object of a homotopy functor. Roughly speaking each transitive Lie algebroids can be described as a vector bundle…
In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($\mathcal{D}$-modules), and reformulate the…
We construct and classify $(1 \; 2\; \cdots \; k)$-twisted $V^{\otimes k}$-modules for $k$ odd and for $V$ a vertex operator superalgebra. This extends previous results of the author, along with Dong and Mason, classifying all…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We give a classification of the graded simple modules of cyclotomic quiver Hecke algebras of type A using the diagram calculus of the diagrammatic Cherednik algebra. We also obtain a non-trivial lower bound for the dimension of the simple…
We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…
In this note we give an account of recent progress on the construction of holomorphic vertex algebras as cyclic orbifolds as well as related topics in lattices and modular categories. We present a novel computation of the Schur indicator of…