The Tetrahedron algebra and its finite-dimensional irreducible modules

Details The Tetrahedron algebra and its finite-dimensional irreducible modules The Tetrahedron algebra and its finite-dimensional irreducible modules

2006-06-08

arxiv.org/abs/math/0606197v1

Mathematics

Representation Theory

18 pages

Scientific paper

Recently 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.

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