Quantum 2 + 1 evolution model

A quantum evolution model in 2 + 1 discrete spacetime, connected with a 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a 2D linear lattice system called 'the current system'. In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical and it corresponds to the known operator-valued R-matrix. The current system is a type of the linear problem for the 2 + 1 evolution model. A generating function for the integrals of motion for the evolution is derived with the help of the current system. Thus, the complete integrability in 3D is proved directly.