The Tetrahedron algebra, the Onsager algebra, and the $\mathfrak{sl}_2$ loop algebra
Hartwig, Brian ; Terwilliger, Paul
arXiv, 0511004 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-11-01
Classification:  Mathematical Physics,  Mathematics - Rings and Algebras,  17B67,  17B81, 82B23 
@article{0511004,
     author = {Hartwig, Brian and Terwilliger, Paul},
     title = {The Tetrahedron algebra, the Onsager algebra, and the $\mathfrak{sl}\_2$
  loop algebra},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511004}
}

Hartwig, Brian; Terwilliger, Paul. The Tetrahedron algebra, the Onsager algebra, and the $\mathfrak{sl}_2$
  loop algebra. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511004/