Vertex algebras and the formal loop space

乘法顶点代数与量子环代数

Multiplicative vertex algebras and quantum loop algebras

本文定义了顶点余代数的乘法版本，证明了 Hall 代数的等变 K 理论构造具有相容的乘法顶点余代数结构，并指出预投射 KHA 猜想同构于某些量子环代数。

On the D-module and formal-variable approaches to vertex algebras

In a program to formulate and develop two-dimensional conformal field theory in the framework of algebraic geometry, Beilinson and Drinfeld have recently given a notion of ``chiral algebra'' in terms of D-modules on algebraic curves. This definition consists of a ``skew-symmetry'' relation and a ``Jacobi identity'' relation in a categorical setting. In this paper, we show directly that these chiral algebras are essentially the same as vertex algebras without vacuum vector (and without grading), by establishing an equivalence between the skew-symmetry and Jacobi identity relations of Beilinson-…

Poisson Vertex Cohomology and Tate Lie Algebroids

We study sheaves on holomorphic spaces of loops and apply this to the study of the complex, defined in \cite{BdSHK}, governing deformations of the \emph{Poisson vertex algebra} structure on the space of holomorphic loops into a Poisson variety. We describe this complex in terms of the (continuous) de Rham-Lie cohomology of an associated Lie algebroid object in locally linearly compact topological (alias \emph{Tate}) sheaves of modules on $\mathcal{L}^{+}M$. In particular this allows us to easily compute the cohomology of the above in the case where $π$ is symplectic - we obtain de Rham cohomol…