Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules

TL;DR

This paper computes the Hochschild cohomology groups of the Weyl conformal algebra with finite module coefficients, extending algebraic discrete Morse theory to differential algebras.

Contribution

It introduces an adaptation of algebraic discrete Morse theory for differential algebras to determine Hochschild cohomology of the Weyl conformal algebra.

Findings

Hochschild cohomology groups are explicitly computed.

The method applies to the Weyl conformal algebra with finite modules.

The approach extends algebraic discrete Morse theory to differential algebra contexts.

Abstract

In this work we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal associative conformal envelope of the Virasoro Lie conformal algebra relative to the locality $N=2$. In order to obtain this result we adjust the algebraic discrete Morse theory to the case of differential algebras.