Related papers: Lagrangian approach to sheaves of vertex algebras

We present a construction of vertex algebra bundles and spaces of conformal blocks over families of logarithmic smooth curves. This work generalizes some earlier results by Frenkel and Ben-Zvi on vertex algebra bundles over complex smooth…

Here we construct spaces of coinvariants for Heisenberg vertex algebras on abelian varieties and show that these globalize to twisted $\mathscr{D}$-modules on the moduli space of abelian varieties. Remarkably, we recover the standard…

We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighborhood of Z, a coherent sheaf on the complement of Z, and an…

In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…

In order to extend the geometrization of Yangian $R$-matrices from Lie algebras $gl(n)$ to superalgebras $gl(M|N)$, we introduce new quiver-related varieties which are associated with representations of $gl(M|N)$. In order to define them…

A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the $\mathfrak{g}$-module $L$ decomposes into copies of the adjoint module, the trivial module,…

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic…

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…

Some natural hidden symmetries in the Verma modules over the Virasoro algebra are constructed in terms of geometric quantization. Their differential geometric meaning is established and their expression via $q_R$-conformal symmetries in the…

We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant…

We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.

We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n spacetime dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the…

We propose two families of differential algebras of classical dimension on kappa-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl super-algebra. We also propose a novel…

An explicit construction is presented for the action of the su(1,1) subalgebra of the Virasoro algebra on path spaces for the c(2,q) minimal models. In the case of the Lee-Yang edge singularity, we show how this action already fixes the…

We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartan's realization problem that applies to both…

We introduce ring theoretic constructions that are similar to the construction of wreath product of groups. In particular, for a given graph $\Gamma=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A\, wr\, L(\Gamma)$ with…

A class of simple filtered Lie algebras of polynomial growth with increasing filtration is distinguished and presentations of these algebras are explicitely described for the simplest examples. Lie (super)algebras of this class appear in…

For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.

Let $A$ be a commutative, associative algebra with unity over $\mathbb{C}$. Using the definition of global Weyl modules for the map superalgebras given by Calixto, Lemay, and Savage we explicitly describe the structure of certain quotients…

The Bershadsky--Polyakov algebras are the subregular quantum hamiltonian reductions of the affine vertex operator algebras associated with $\mathfrak{sl}_3$. In arXiv:2007.00396 [math.QA], we realised these algebras in terms of the regular…