A. V. Odesskii, “Bihamiltonian elliptic structures”, Mosc. Math. J., 2004, Volume 4, Number 4,Pages <nobr>941

This article is cited in 6 papers

Bihamiltonian elliptic structures

A. V. Odesskii^ab

^a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
^b Institut des Hautes Études Scientifiques

Abstract: We construct three compatible quadratic Poisson structures such that generic linear combination of them is associated with elliptic Sklyanin algebra in $n$ generators. Symplectic leaves of this elliptic Poisson structure is studied. Explicit formulas for Casimir elements are obtained.

Key words and phrases: Bihamitonian structure, Lenard scheme, elliptic algebras, symplectic leaves, Casimir elements.

MSC: 14, 79

Received: January 6, 2003

Language: English

DOI: 10.17323/1609-4514-2004-4-4-941-946