Lattice integrals of motion of the Ising model on the cylinder

► We consider the transfer matrix of the critical Ising model with spatially periodic boundary conditions. ► We introduce lattice integrals of motion built from the Temperley-Lieb algebra and use them to decompose the transfer matrix. ► We find a relation between eigenvalues of the lattice integrals of motion and local integrals of motion of conformal field theory.