Functorial constructions related to double Poisson vertex algebras
Representation Theory
2025-09-26 v2 Algebraic Geometry
Rings and Algebras
Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.2307.06071,
title = {Functorial constructions related to double Poisson vertex algebras},
author = {Tristan Bozec and Maxime Fairon and Anne Moreau},
journal= {arXiv preprint arXiv:2307.06071},
year = {2025}
}
Comments
v2: 66 pages, accepted version. Minor revisions and Section 3 has been shortened