Multidimensional multiplicative Poisson vertex algebras
Pengfei Yang, Matteo Casati

TL;DR
This paper introduces multidimensional multiplicative Poisson vertex algebras, generalizing existing structures to difference algebras with multiple shifts, and explores their relation to Hamiltonian difference operators and bi-Hamiltonian pairs.
Contribution
It defines the multidimensional multiplicative Poisson vertex algebra and characterizes scalar local Hamiltonian difference operators up to order (-2,2).
Findings
Established the equivalence to Hamiltonian difference operators.
Characterized scalar local Hamiltonian difference operators.
Investigated bi-Hamiltonian pairs in this context.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
