Finite dimensional modules for the \(q\)-tetrahedron algebra

zbMath1232.17026MaRDI QIDQ987174

Kei Miki

Publication date: 13 August 2010

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1277298918

zbMATH Keywords

quantizationLie algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (10)

Tridiagonal pairs of q-Racah type, the Bockting operator ψ, and L-operators for U_q(L(sl_2)) ⋮ Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view ⋮ Finite-dimensional irreducible \(\square_q\)-modules and their Drinfel'd polynomials ⋮ Some \(q\)-exponential formulas for finite-dimensional \(\square_q\)-modules ⋮ Evaluation modules for the \(q\)-tetrahedron algebra ⋮ The \(q\)-Onsager algebra and the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\) ⋮ Bidiagonal triples ⋮ Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra ⋮ Double lowering operators on polynomials ⋮ Leonard pairs having zero-diagonal TD-TD form

Cites Work

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• Solutions of the Yang-Baxter equation
• The tetrahedron algebra and its finite-dimensional irreducible modules
• The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra
• Tridiagonal pairs and the \(q\)-tetrahedron algebra
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Quantum affine algebras
• Braid group action and quantum affine algebras
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• The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra
• The universal central extension of the three-point $\mathfrak {sl}_2$ loop algebra
• TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS
• Generalized Affine Kac-Moody Lie Algebras Over Localizations of the Polynomial Ring in One Variable
• Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra
• Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules
• The $S_4$-action on tetrahedron algebra

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