The Tetrahedron algebra, the Onsager algebra, and the $\mathfrak{sl}_2$ loop algebra

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dc.creatorHartwig, Brian
dc.creatorTerwilliger, Paul
dc.date2005-11-02
dc.date.accessioned2026-07-07T06:50:26Z
dc.date.available2026-07-07T06:50:26Z
dc.descriptionLet $K$ 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.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0511004
dc.identifierhttp://arxiv.org/abs/math-ph/0511004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104669
dc.subjectMathematical Physics
dc.subjectRings and Algebras
dc.subject17B67; 17B81, 82B23
dc.titleThe Tetrahedron algebra, the Onsager algebra, and the $\mathfrak{sl}_2$ loop algebra
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