On algebro-geometric Poisson brakets for the Volterra lattice

A generalization of the theory of algebro-geometric Poisson brackets on the space of finite-gap Schrodinger operators, developped by S.P.Novikov and A.P.Veselov, to the case of periodic zero-diagonal difference operators of second order is proposed. A necessary and sufficient condition for such a bracket to be compatible with higher Volterra flows is found.