New noncommutative Yang-Baxter and tetrahedron maps for Boussinesq and NLS type systems are constructed and proven to satisfy the defining simplex equations.
Algebraic integrable dynamical systems, 2+1-dimensional models in wholly discrete space-time, and inhomogeneous models in 2-dimensional statistical physics
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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.
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Noncommutative Boussinesq and NLS type 2- and 3-simplex maps
New noncommutative Yang-Baxter and tetrahedron maps for Boussinesq and NLS type systems are constructed and proven to satisfy the defining simplex equations.