Advances in Mathematical Physics
Volume 2011 (2011), Article ID 252186, 18 pages
Research Article

Integer Solutions of Integral Inequalities and 𝐻 -Invariant Jacobian Poisson Structures

1Dipartimento di Matematica Pura e Applicazioni, Università degli Milano Bicocca, Via R.Cozzi 53, 20125 Milano, Italy
2Département de Mathématiques 2, Laboratoire Angevin de Recherche en Mathématiques Université D'Angers, boulevard Lavoisier, 49045 Angers, France
3Mathematics Research Unit at Luxembourg, University of Luxembourg, 6 rue Richard Coudenhove-Kalergi, 1359 Luxembourg City, Luxembourg

Received 14 April 2011; Accepted 3 June 2011

Academic Editor: Yao-Zhong Zhang

Copyright © 2011 G. Ortenzi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.