English

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}
}

Comments

27 pages

R2 v1 2026-07-01T08:13:27.592Z