On classification of Poisson vertex algebras

TL;DR

This paper discusses a conjectural framework for classifying Poisson vertex algebras, focusing on those of CFT type and scalar Hamiltonian operators, aiming to organize their structure systematically.

Contribution

It introduces a conjectural classification scheme for Poisson vertex algebras of specific types, advancing understanding of their structural organization.

Findings

Proposes a classification conjecture for Poisson vertex algebras

Focuses on algebras of CFT type and scalar Hamiltonian operators

Lays groundwork for future rigorous classification proofs

Abstract

We describe a conjectural classification of Poisson vertex algebras of CFT type and of Poisson vertex algebras in one differential variable (= scalar Hamiltonian operators).