The Tetrahedron algebra, the Onsager algebra, and the \mathfraksl₂ loop algebra

2005/11/02 by Hartwig, Brian, Terwilliger, Paul
#17B67 #17B81 #82B23 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.math-ph/0511004

Abstract

Let K denote a field with characteristic 0 and let T denote an indeterminate. We give a presentation for the three-point loop algebra \mathfraksl₂ ⊗ K\lbrack T, T^-1,(T-1)^-1\rbrack via generators and relations. This presentation displays S₄-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.

Related

• The Universal Central Extension of the Three-point sl₂ Loop Algebra
• The Onsager Algebra
• Extension of a Borel subalgebra symmetry into the sl(2) loop algebra symmetry for the twisted XXZ spin chain at roots of unity and the Onsager algebra
• The Tetrahedron algebra and its finite-dimensional irreducible modules
• The S₄-action on the Tetrahedron algebra