Algebraic integrable dynamical systems, 2+1-dimensional models in wholly discrete space-time, and inhomogeneous models in 2-dimensional statistical physics

Abstract

This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in 2+1-dimensional wholly discrete space-time, and to connection between those field theories and inhomogoneous models in 2-dimensional statistical physics.