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

Abstract

Characteristic Lie rings for Toda type 2+1 dimensional lattices are defined. Some properties of these rings are studied. Infinite sequence of special kind modules are introduced. It is proved that for known integrable lattices these modules are finitely generated. Classification algorithm based on this observation is briefly discussed.

11 pages

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