Functorial constructions related to double Poisson vertex algebras

TL;DR

This paper introduces a jet algebra construction to produce double Poisson vertex algebras from double Poisson algebras, explores their compatibility with representation functors, and provides examples including double quivers.

Contribution

It presents a novel jet algebra construction for double Poisson vertex algebras and analyzes their relations with representation, reduction, and Hamiltonian reduction functors.

Findings

Construction of double Poisson vertex algebras from double Poisson algebras

Compatibility with representation functors for Poisson and vertex algebras

Examples derived from double quivers

Abstract

For any double Poisson algebra, we produce a double Poisson vertex algebra using the jet algebra construction. We show that this construction is compatible with the representation functor which associates to any double Poisson (vertex) algebra and any positive integer a Poisson (vertex) algebra. We also consider related constructions, such as Poisson reductions and Hamiltonian reductions, with the aim of comparing the different corresponding categories. This allows us to provide various interesting examples of double Poisson vertex algebras, in particular from double quivers.