2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56651A generalization of the theory of algebro-geometric Poisson brackets on the space of finite-gap Schroedinger 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.8 pages, written addendumMathematical PhysicsAlgebraic GeometryExactly Solvable and Integrable Systems34G20, 34L40text