Compatible Poisson Structures of Toda Type Discrete Hierarchy

Abstract

An algebra isomorphism between algebras of matrices and difference operators is used to investigate the discrete integrable hierarchy. We find local and non-local families of R-matrix solutions to the modified Yang-Baxter equation. The three R-theoretic Poisson structures and the Suris quadratic bracket are derived. The resulting family of bi-Poisson structures include a seminal discrete bi-Poisson structure of Kupershmidt at a special value.

22 pages, LaTeX, v3: Minor changes

References in corpus (1)

• Generalized fermionic discrete Toda hierarchy

Cited by in corpus (2)

• Fermionic one- and two-dimensional Toda lattice hierarchies and their bi-Hamiltonian structures
• Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies