First integrals and stationary states for quantum Heisenberg spin dynamics

Problem of the existence of the first integrals and stationary states with respect to one-parameter group of automorphisms of $C^*$-algebra of quasilocal observables is studied in the case of a quantum spin system with arbitrary spin on a $\nu$-dimensional integer lattice generated by the potential of the isotropic Heisenberg model with the interaction of nearest neighbours.