SL(N) ONSAGERS ALGEBRA AND INTEGRABILITY

We define an sl(N) analog of Onsager's algebra through a finite set of relations that generalize the Dolan-Grady defining relations for the original Onsager's algebra. This infinite-dimensional Lie algebra is s hown to be isomorphic to a fixed-point subalgebra of sl(N) loop algebr a with respect to a certain involution. As the consequence of the gene ralized Dolan-Grady relations a Hamiltonian linear in the generators o f sl(N) Onsager's algebra is shown to possess an infinite number of mu tually commuting integrals of motion.