# Computation of cohomology of Lie conformal and Poisson vertex algebras

## TL;DR

This paper develops methods to compute the cohomology of Poisson vertex algebras, providing explicit calculations for various algebra types and establishing finite dimensionality under certain conditions.

## Contribution

It introduces new computational techniques for Poisson vertex algebra cohomology and applies them to key algebra classes, proving finite dimensionality in specific cases.

## Key findings

- Cohomology computed for free bosonic and fermionic Poisson vertex (super)algebras
- Cohomology computed for universal affine and Virasoro Poisson vertex algebras
- Finite dimensionality established for finitely and freely generated conformal Poisson vertex (super)algebras

## Abstract

We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. We establish finite dimensionality of this cohomology for conformal Poisson vertex (super)algebras that are finitely and freely generated by elements of positive conformal weight.