2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104669Let $K$ denote a field with characteristic 0 and let $T$ denote an indeterminate. We give a presentation for the three-point loop algebra $\mathfrak{sl}_2 \otimes K\lbrack T, T^{-1},(T-1)^{-1}\rbrack$ via generators and relations. This presentation displays $S_4$-symmetry. Using this presentation we obtain a decomposition of the above loop algebra into a direct sum of three subalgebras, each of which is isomorphic to the Onsager algebra.25 pagesMathematical PhysicsRings and Algebras17B67; 17B81, 82B23text