Multidimensional multiplicative Poisson vertex algebras
Exactly Solvable and Integrable Systems
2025-12-09 v1
Abstract
In this paper we introduce the notion of multidimensional multiplicative Poisson vertex algebra, the generalization of the notion of multiplicative Poisson vertex algebra to a difference algebra endowed with D commuting shifts. After showing the equivalence of this notion to the notion of Hamiltonian difference operator on a D-dimensional lattice, we characterize scalar local Hamiltonian difference operators up to the order (-2,2) and investigate the bi-Hamiltonian pairs they form.
Keywords
Cite
@article{arxiv.2512.06704,
title = {Multidimensional multiplicative Poisson vertex algebras},
author = {Pengfei Yang and Matteo Casati},
journal= {arXiv preprint arXiv:2512.06704},
year = {2025}
}
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27 pages