Abstract
We define ansl(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 shown to be isomorphic to a fixed-point subalgebra ofsl(N) loop algebra with respect to a certain involution. As the consequence of the generalized Dolan-Grady relations a Hamiltonian linear in the generators ofsl(N) Onsager's algebra is shown to posses an infinite number of mutually commuting integrals of motion.
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Uglov, D.B., Ivanov, I.T. sl(N) Onsager's algebra and integrability. J Stat Phys 82, 87–113 (1996). https://doi.org/10.1007/BF02189226
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DOI: https://doi.org/10.1007/BF02189226