The Negative Relativistic Toda Hierarchy and Rational Poisson Brackets

Joana M. Nunes da Costa and Pantelis A. Damianou

We define hierarchies for negative values of the index of Poisson tensors, master symmetries and Hamiltonians for the finite, nonperiodic, relativistic Toda lattice. We show that the usual relations between master symmetries, Poisson tensors and invariants hold over all integer values of the index.