Characteristic Lie rings, finitely-generated modules and integrability conditions for (2 + 1)-dimensional lattices

摘要

Characteristic Lie rings for Toda and Volterra type (2 + 1)-dimensional lattices are defined. Some properties of these rings are studied. Infinite sequence of special kind subrings are introduced. It is proved that for known integrable lattices these subrings are of finite dimension. A classification algorithm based on this observation is suggested.