Compatible quadratic Poisson brackets related to a family of elliptic curves
Abstract
We construct nine pairwise compatible quadratic Poisson structures such that a generic linear combination of them is associated with an elliptic algebra in n generators. Explicit formulas for Casimir elements of this elliptic Poisson structure are obtained.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- January 2013
- DOI:
- 10.1016/j.geomphys.2012.10.004
- arXiv:
- arXiv:1204.1299
- Bibcode:
- 2013JGP....63..107O
- Keywords:
-
- Mathematics - Quantum Algebra;
- Mathematics - Algebraic Geometry;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 17 pages, Latex, major changes