Non-local Hamiltonian structures and applications to the theory of   integrable systems I
  We develop a rigorous theory of non-local Hamiltonian structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard-Magri scheme of integrability to a pair of compatible non-local Hamiltonian structures. 
Alberto De Sole and Victor G. Kac
math-ph math.MP math.RA math.RT