# Poisson vertex algebra cohomology and differential Harrison cohomology

## TL;DR

This paper establishes a canonical connection between Poisson vertex algebra cohomology and differential Harrison cohomology, advancing the understanding of their relationship and aiding in cohomology computations.

## Contribution

It constructs a canonical map linking Poisson vertex algebra cohomology to differential Harrison cohomology, which is an important step in their computation.

## Key findings

- The map restricts to an isomorphism in top degree.
- Facilitates computation of Poisson vertex algebra cohomology.
- Provides a new tool for studying vertex algebra structures.

## Abstract

We construct a canonical map from the Poisson vertex algebra cohomology complex to the differential Harrison cohomology complex, which restricts to an isomorphism on the top degree. This is an important step in the computation of Poisson vertex algebra and vertex algebra cohomologies.