Multidimensional multiplicative Poisson vertex algebras

Pengfei Yang; Matteo Casati

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arXiv · 2512.06704

Multidimensional multiplicative Poisson vertex algebras

Pengfei Yang·Matteo Casati

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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.

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BibTeX RIS

Pengfei Yang, Matteo Casati. 2025-12-07. Multidimensional multiplicative Poisson vertex algebras. https://arxiv.org/abs/2512.06704

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