The q-tetrahedron algebra and its finite dimensional irreducible modules

2006/02/09 by Tatsuro Ito, Paul Terwilliger, Ito, Tatsuro +1
Mathematics · Physics and Astronomy · #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0602199

openalex publication_date 2006/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently B. Hartwig and the second author found a presentation for the three-point sl₂ loop algebra via generators and relations. To obtain this presentation they defined an algebra \boxtimes by generators and relations, and displayed an isomorphism from \boxtimes to the three-point sl₂ loop algebra. We introduce a quantum analog of \boxtimes which we call \boxtimes_q. We define \boxtimes_q via generators and relations. We show how \boxtimes_q is related to the quantum group U_q(sl₂), the U_q(sl₂) loop algebra, and the positive part of U_q(sl₂). We describe the finite dimensional irreducible \boxtimes_q-modules under the assumption that q is not a root of 1, and the underlying field is algebraically closed.

Citations

• Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

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