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Advances in Mathematical Physics
Volume 2011 (2011), Article ID 252186, 18 pages
Integer Solutions of Integral Inequalities and -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.
- A. V. Odesskiĭ and V. N. Rubtsov, “Polynomial Poisson algebras with a regular structure of symplectic leaves,” Teoreticheskaya i Matematicheskaya Fizika, vol. 133, no. 1, pp. 3–23, 2002 (Russian).
- G. Ortenzi, V. Rubtsov, and S. R. T. Pelap, “On the Heisenberg invariance and the elliptic poisson tensors,” Letters in Mathematical Physics, vol. 96, no. 1–3, pp. 263–284, 2011.
- G. Ortenzi, V. Rubtsov, T. Pelap, and S. Roméo, “Elliptic Sklyanin Algebras and projective geometry of elliptic curves in and ,” unpublished.
- A. V. Odesskiĭ, “Elliptic algebras,” Russian Mathematical Survey, 2005 (Russian).
- L. Takhtajan, “On foundation of the generalized Nambu mechanics,” Communications in Mathematical Physics, vol. 160, no. 2, pp. 295–315, 1994.
- Y. Nambu, “Generalized Hamiltonian dynamics,” Physical Review D, vol. 7, pp. 2405–2412, 1973.
- G. Khimshiashvili, “On one class of exact Poisson structures,” Georgian Academy of Sciences. Proceedings of A. Razmadze Mathematical Institute, vol. 119, pp. 111–120, 1999.
- G. Khimshiashvili and R. Przybysz, “On generalized Sklyanin algebras,” Georgian Mathematical Journal, vol. 7, no. 4, pp. 689–700, 2000.
- S. R. T. Pelap, “Poisson (co)homology of polynomial Poisson algebras in dimension four: Sklyanin's case,” Journal of Algebra, vol. 322, no. 4, pp. 1151–1169, 2009.
- E. K. Sklyanin, “Some algebraic structures connected with the Yang-Baxter equation,” Funktsional'nyi Analiz i Ego Prilozheniya, vol. 16, no. 4, pp. 27–34, 1982 (Russian).
- E. K. Sklyanin, “Some algebraic structures connected with the Yang-Baxter equation. Representations of a quantum algebra,” Funktsional'nyi Analiz i Ego Prilozheniya, vol. 17, no. 4, pp. 34–48, 1983 (Russian).
- B. L. Feĭgin and A. V. Odesskiĭ, “Vector bundles on an elliptic curve and Sklyanin algebras,” in Topics in Quantum Groups and Finite-Type Invariants, vol. 185 of American Mathematical Society Translations: Series 2, pp. 65–84, American Mathematical Society, Providence, RI, USA, 1998.
- A. V. Odesskiĭ and B. L. Feĭgin, “Sklyanin's elliptic algebras,” Akademiya Nauk SSSR, vol. 23, no. 3, pp. 45–54, 1989 (Russian), translation in Functional Analysis and Its Applications, vol. 23, no. 3, pp. 207–214, 1989.
- A. Pichereau, “Poisson (co)homology and isolated singularities,” Journal of Algebra, vol. 299, no. 2, pp. 747–777, 2006.
- P. Etingof and V. Ginzburg, “Noncommutative del Pezzo surfaces and Calabi-Yau algebras,” JEMS: Journal of the European Mathematical Society, vol. 12, no. 6, pp. 1371–1416, 2010.
- I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Mathematical Modelling: Theory and Applications, Birkhäuser, Boston, Mass, USA, 1994.
- A. Barvinok, Integer Points in Polyhedra, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, Switzerland, 2008.
- M. Beck and S. Robins, Computing the Continuous Discretely, Undergraduate Texts in Mathematics, Springer, New York, NY, USA, 2007.
- S. Corteel, S. Lee, and C. D. Savage, “Five guidelines for partition analysis with applications to lecture hall-type theorems,” in Combinatorial Number Theory, pp. 131–155, de Gruyter, Berlin, Germany, 2007.