Bi-Hamiltonian structure of the Oriented Associativity equation

none2siThe Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equa- tion, besides being Hamiltonian with respect to a first-order Hamilto- nian operator, has a third-order non-local homogeneous Hamiltonian operator belonging to a class which has been recently studied, thus providing a highly non-trivial example in that class and showing in- triguing connections with algebraic geometry.restrictedPavlov, Maxim V; Vitolo, RaffaelePavlov, Maxim V; Vitolo, Raffael