Functional Tetrahedron Equation
  We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest the symmetries of a model in local form. We construct a very general "block-matrix model" together with its algebro-geometric solutions, study its various particular cases, and also present a remarkably simple scheme of quantization for one of those cases. 
R.M. Kashaev, I.G. Korepanov, S.M. Sergeev