%0 Journal Article
%T The Tetrahedron algebra, the Onsager algebra, and the $\mathfrak{sl}_2$ loop algebra
%A Brian Hartwig
%A Paul Terwilliger
%J Mathematics
%D 2005
%I arXiv
%X Let $K$ 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.
%U http://arxiv.org/abs/math-ph/0511004v1