Integer solutions of integral inequalities and H-invariant Jacobian Poisson structures

TL;DR

This paper investigates Jacobian Poisson structures invariant under the discrete Heisenberg group across various dimensions, focusing on classification and specific examples like Artin-Schelter-Tate tensors, with implications for integral inequalities and discrete volume calculations.

Contribution

It provides a classification framework for H-invariant Jacobian Poisson structures and explores their connections to integral inequalities and discrete geometric volumes.

Findings

Classification of H-invariant Jacobian Poisson structures in multiple dimensions

Identification of the Artin-Schelter-Tate Poisson tensors as key examples

Link between structure classification and discrete volume of solids

Abstract

We study the Jacobian Poisson structures in any dimension invariant with respect to the discrete Heisenberg group. The classification problem is related to the discrete volume of suitable solids. Particular attention is given to dimension 3 whose simplest example is the Artin-Schelter-Tate Poisson tensors respectively.