2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113820Recently Terwilliger and the present author found a presentation for the three-point $\mathfrak{sl}_2$ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra $\boxtimes$ by generators and relations and displayed an isomorphism from $\boxtimes$ to the three-point $\mathfrak{sl}_2$ loop algebra. In this paper we classify the finite-dimensional irreducible $\boxtimes$-modules.18 pagesRepresentation TheoryCombinatoricstext