sl(N) Onsager's algebra and integrability |
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Authors: | D. B. Uglov I. T. Ivanov |
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Affiliation: | (1) Institute for Theoretical Physics, State University of New York at Stony Brook, 11794-3840 Stony Brook, New York |
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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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Keywords: | Onsager's algbera loop algebras Ising model integrability |
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