Equations of motion and conserved quantities in non-Abelian discrete integrable models

Conserved quantities for the Hirota bilinear difference equation, which is satisfied by eigenvalues of the transfer matrix, are studied. The transfer-matrix eigenvalue combinations that are integrals of motion for discrete integrable models, which correspond to $A_{k-1}$ algebras and satisfy zero or quasi-periodic boundary conditions, are found. Discrete equations of motion for a non-Abelian generalization of the Liouville model and the discrete analogue of the Tsitseiko equation are obtained.